diff --git a/.gitignore b/.gitignore
index f99a270896772a45cfda53ef7ee29a70b209488c..cf83860fb1f3e75f439e0287a26ba59b8de3288a 100644
--- a/.gitignore
+++ b/.gitignore
@@ -10,3 +10,4 @@ data*.dat
determinant.pdf
fig?.jpg
perturbative.pdf
+determinant-v1.1.pdf
diff --git a/Math and checks.nb b/Math and checks.nb
index 4c158bbcdea3e700b713be14943fb40b751cc3e3..cc6ca03663d30f549e73f9e631e2503253d0c5a2 100644
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diff --git a/Toeplitz determinant.nb b/Toeplitz determinant.nb
index 492ede7cda5ae81cefce132580bee8d5cce430b6..b3b18fe838d8e1b77ce6e693c7c8a9c2efda15a4 100644
--- a/Toeplitz determinant.nb
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+9rH4+MsUodiS9iqIkmavJcxo2V6FuS7+mjpyToWDvr/m7Zll3q5C0oDAz7qf
+NU+N3mZN8qFx2qtRM3XX+GSMNadG0Mr49VmttFfjjsNL7hMttI+DIVzWPtqp
+lfwLf3zuDg==
+ "]]}}, {{
+ Directive[
+ PointSize[0.007333333333333334],
+ RGBColor[0.368417, 0.506779, 0.709798],
+ AbsoluteThickness[1.6]]}, {
+ Directive[
+ PointSize[0.007333333333333334],
+ RGBColor[0.880722, 0.611041, 0.142051],
+ AbsoluteThickness[1.6]]}, {
+ Directive[
+ PointSize[0.007333333333333334],
+ RGBColor[0.560181, 0.691569, 0.194885],
+ AbsoluteThickness[1.6]]}, {}, {}, {}, {}, {}, {}, {}}, {{
+ Directive[
+ PointSize[0.007333333333333334],
+ RGBColor[0.368417, 0.506779, 0.709798],
+ AbsoluteThickness[1.6]]}, {
+ Directive[
+ PointSize[0.007333333333333334],
+ RGBColor[0.880722, 0.611041, 0.142051],
+ AbsoluteThickness[1.6]]}, {
+ Directive[
+ PointSize[0.007333333333333334],
+ RGBColor[0.560181, 0.691569, 0.194885],
+ AbsoluteThickness[
+ 1.6]]}, {}, {}, {}, {}, {}, {}, {}}}, {{}, {}}}}, {
+ DisplayFunction -> Identity, Ticks -> {Automatic, Automatic},
+ AxesOrigin -> {1., 0}, FrameTicks -> {{Automatic,
+ Charting`ScaledFrameTicks[{Identity, Identity}]}, {Automatic,
+ Charting`ScaledFrameTicks[{Identity, Identity}]}},
+ GridLines -> {None, None}, DisplayFunction -> Identity,
+ PlotRangePadding -> {{
+ Scaled[0.02],
+ Scaled[0.02]}, {
+ Scaled[0.05],
+ Scaled[0.05]}}, PlotRangeClipping -> True, ImagePadding -> All,
+ DisplayFunction -> Identity, AspectRatio ->
NCache[GoldenRatio^(-1), 0.6180339887498948], Axes -> {True, True},
AxesLabel -> {None, None}, AxesOrigin -> {0, 0}, DisplayFunction :>
Identity, Frame -> {{False, False}, {False, False}},
@@ -2074,8 +3631,16 @@ rCAgOoN6LhZ6uWosrXTqD6IqXFNaeeCKw3+A4dYQ
GridLines -> {None, None}, GridLinesStyle -> Directive[
GrayLevel[0.5, 0.4]],
Method -> {
- "OptimizePlotMarkers" -> True,
- "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
+ "DefaultBoundaryStyle" -> Automatic,
+ "DefaultGraphicsInteraction" -> {
+ "Version" -> 1.2, "TrackMousePosition" -> {True, False},
+ "Effects" -> {
+ "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2},
+ "Droplines" -> {
+ "freeformCursorMode" -> True,
+ "placement" -> {"x" -> "All", "y" -> "None"}}}},
+ "DefaultMeshStyle" -> AbsolutePointSize[6], "ScalingFunctions" -> None,
+ "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
(Identity[#]& )[
Part[#, 1]],
(Identity[#]& )[
@@ -2084,127 +3649,118 @@ rCAgOoN6LhZ6uWosrXTqD6IqXFNaeeCKw3+A4dYQ
Part[#, 1]],
(Identity[#]& )[
Part[#, 2]]}& )}},
- PlotRange -> {{0, 100.}, {-0.3154585682788162, 0.9802175369809089}},
+ PlotRange -> {{1, 100}, {-0.5031305176228675, 0.6862897676952574}},
PlotRangeClipping -> True, PlotRangePadding -> {{
Scaled[0.02],
Scaled[0.02]}, {
- Scaled[0.05],
- Scaled[0.05]}}, Ticks -> {Automatic, Automatic}}],FormBox[
- FormBox[
- TemplateBox[{"\"Re\"", "\"Im\"", "\"Abs\""}, "PointLegend",
- DisplayFunction -> (FormBox[
- StyleBox[
- StyleBox[
- PaneBox[
- TagBox[
- GridBox[{{
- TagBox[
- GridBox[{{
- GraphicsBox[{{}, {
+ Scaled[0.02],
+ Scaled[0.02]}}, Ticks -> {Automatic, Automatic}}],FormBox[
+ TagBox[
+ GridBox[{{
+ FormBox[
+ TemplateBox[{"\"Re1\"", "\"Im1\"", "\"Abs1\""}, "LineLegend",
+ DisplayFunction -> (StyleBox[
+ StyleBox[
+ PaneBox[
+ TagBox[
+ GridBox[{{
+ TagBox[
+ GridBox[{{
+ GraphicsBox[{{
Directive[
EdgeForm[
Directive[
Opacity[0.3],
GrayLevel[0]]],
PointSize[0.5],
+ Opacity[1.],
RGBColor[0.368417, 0.506779, 0.709798],
AbsoluteThickness[1.6]], {
+ LineBox[{{0, 10}, {20, 10}}]}}, {
Directive[
EdgeForm[
Directive[
Opacity[0.3],
GrayLevel[0]]],
PointSize[0.5],
+ Opacity[1.],
RGBColor[0.368417, 0.506779, 0.709798],
- AbsoluteThickness[1.6]],
- PointBox[
- NCache[{
- Scaled[{
- Rational[1, 2],
- Rational[1, 2]}]}, {
- Scaled[{0.5, 0.5}]}]]}}}, AspectRatio -> Full,
- ImageSize -> {10, 10}, PlotRangePadding -> None,
+ AbsoluteThickness[1.6]], {}}}, AspectRatio -> Full,
+ ImageSize -> {20, 10}, PlotRangePadding -> None,
ImagePadding -> Automatic,
BaselinePosition -> (Scaled[0.1] -> Baseline)], #}, {
- GraphicsBox[{{}, {
+ GraphicsBox[{{
Directive[
EdgeForm[
Directive[
Opacity[0.3],
GrayLevel[0]]],
PointSize[0.5],
+ Opacity[1.],
RGBColor[0.880722, 0.611041, 0.142051],
AbsoluteThickness[1.6]], {
+ LineBox[{{0, 10}, {20, 10}}]}}, {
Directive[
EdgeForm[
Directive[
Opacity[0.3],
GrayLevel[0]]],
PointSize[0.5],
+ Opacity[1.],
RGBColor[0.880722, 0.611041, 0.142051],
- AbsoluteThickness[1.6]],
- PointBox[
- NCache[{
- Scaled[{
- Rational[1, 2],
- Rational[1, 2]}]}, {
- Scaled[{0.5, 0.5}]}]]}}}, AspectRatio -> Full,
- ImageSize -> {10, 10}, PlotRangePadding -> None,
+ AbsoluteThickness[1.6]], {}}}, AspectRatio -> Full,
+ ImageSize -> {20, 10}, PlotRangePadding -> None,
ImagePadding -> Automatic,
BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}, {
- GraphicsBox[{{}, {
+ GraphicsBox[{{
Directive[
EdgeForm[
Directive[
Opacity[0.3],
GrayLevel[0]]],
PointSize[0.5],
+ Opacity[1.],
RGBColor[0.560181, 0.691569, 0.194885],
AbsoluteThickness[1.6]], {
+ LineBox[{{0, 10}, {20, 10}}]}}, {
Directive[
EdgeForm[
Directive[
Opacity[0.3],
GrayLevel[0]]],
PointSize[0.5],
+ Opacity[1.],
RGBColor[0.560181, 0.691569, 0.194885],
- AbsoluteThickness[1.6]],
- PointBox[
- NCache[{
- Scaled[{
- Rational[1, 2],
- Rational[1, 2]}]}, {
- Scaled[{0.5, 0.5}]}]]}}}, AspectRatio -> Full,
- ImageSize -> {10, 10}, PlotRangePadding -> None,
+ AbsoluteThickness[1.6]], {}}}, AspectRatio -> Full,
+ ImageSize -> {20, 10}, PlotRangePadding -> None,
ImagePadding -> Automatic,
BaselinePosition -> (Scaled[0.1] -> Baseline)], #3}},
- GridBoxAlignment -> {
- "Columns" -> {Center, Left}, "Rows" -> {{Baseline}}},
- AutoDelete -> False,
- GridBoxDividers -> {
- "Columns" -> {{False}}, "Rows" -> {{False}}},
- GridBoxItemSize -> {"Columns" -> {{All}}, "Rows" -> {{All}}},
- GridBoxSpacings -> {
- "Columns" -> {{0.5}}, "Rows" -> {{0.8}}}], "Grid"]}},
- GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}},
- AutoDelete -> False,
- GridBoxItemSize -> {
- "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}},
- GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}],
- "Grid"], Alignment -> Left, AppearanceElements -> None,
- ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction ->
- "ResizeToFit"], LineIndent -> 0, StripOnInput -> False], {
- FontFamily -> "Arial"}, Background -> Automatic, StripOnInput ->
- False], TraditionalForm]& ),
- InterpretationFunction :> (RowBox[{"PointLegend", "[",
- RowBox[{
- RowBox[{"{",
+ GridBoxAlignment -> {
+ "Columns" -> {Center, Left}, "Rows" -> {{Baseline}}},
+ AutoDelete -> False,
+ GridBoxDividers -> {
+ "Columns" -> {{False}}, "Rows" -> {{False}}},
+ GridBoxItemSize -> {
+ "Columns" -> {{All}}, "Rows" -> {{All}}},
+ GridBoxSpacings -> {
+ "Columns" -> {{0.5}}, "Rows" -> {{0.8}}}], "Grid"]}},
+ GridBoxAlignment -> {
+ "Columns" -> {{Left}}, "Rows" -> {{Top}}}, AutoDelete ->
+ False, GridBoxItemSize -> {
+ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}},
+ GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}],
+ "Grid"], Alignment -> Left, AppearanceElements -> None,
+ ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction ->
+ "ResizeToFit"], LineIndent -> 0, StripOnInput -> False], {
+ FontFamily -> "Arial"}, Background -> Automatic, StripOnInput ->
+ False]& ), InterpretationFunction :> (RowBox[{"LineLegend", "[",
RowBox[{
- RowBox[{"Directive", "[",
+ RowBox[{"{",
RowBox[{
- RowBox[{"PointSize", "[", "0.007333333333333334`", "]"}],
- ",",
- InterpretationBox[
+ RowBox[{"Directive", "[",
+ RowBox[{
+ RowBox[{"Opacity", "[", "1.`", "]"}], ",",
+ InterpretationBox[
ButtonBox[
TooltipBox[
GraphicsBox[{{
@@ -2220,8 +3776,7 @@ rCAgOoN6LhZ6uWosrXTqD6IqXFNaeeCKw3+A4dYQ
0.24561133333333335`, 0.3378526666666667,
0.4731986666666667], FrameTicks -> None, PlotRangePadding ->
None, ImageSize ->
- Dynamic[{
- Automatic, 1.35 CurrentValue["FontCapHeight"]/
+ Dynamic[{Automatic, 1.35 CurrentValue["FontCapHeight"]/
AbsoluteCurrentValue[Magnification]}]],
StyleBox[
RowBox[{"RGBColor", "[",
@@ -2248,13 +3803,12 @@ rCAgOoN6LhZ6uWosrXTqD6IqXFNaeeCKw3+A4dYQ
Automatic, Method -> "Preemptive"],
RGBColor[0.368417, 0.506779, 0.709798], Editable -> False,
Selectable -> False], ",",
- RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}], "]"}],
- ",",
- RowBox[{"Directive", "[",
- RowBox[{
- RowBox[{"PointSize", "[", "0.007333333333333334`", "]"}],
+ RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}], "]"}],
",",
- InterpretationBox[
+ RowBox[{"Directive", "[",
+ RowBox[{
+ RowBox[{"Opacity", "[", "1.`", "]"}], ",",
+ InterpretationBox[
ButtonBox[
TooltipBox[
GraphicsBox[{{
@@ -2269,8 +3823,7 @@ rCAgOoN6LhZ6uWosrXTqD6IqXFNaeeCKw3+A4dYQ
RGBColor[
0.587148, 0.40736066666666665`, 0.09470066666666668],
FrameTicks -> None, PlotRangePadding -> None, ImageSize ->
- Dynamic[{
- Automatic, 1.35 CurrentValue["FontCapHeight"]/
+ Dynamic[{Automatic, 1.35 CurrentValue["FontCapHeight"]/
AbsoluteCurrentValue[Magnification]}]],
StyleBox[
RowBox[{"RGBColor", "[",
@@ -2297,13 +3850,274 @@ rCAgOoN6LhZ6uWosrXTqD6IqXFNaeeCKw3+A4dYQ
Automatic, Method -> "Preemptive"],
RGBColor[0.880722, 0.611041, 0.142051], Editable -> False,
Selectable -> False], ",",
- RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}], "]"}],
- ",",
- RowBox[{"Directive", "[",
+ RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}], "]"}],
+ ",",
+ RowBox[{"Directive", "[",
+ RowBox[{
+ RowBox[{"Opacity", "[", "1.`", "]"}], ",",
+ InterpretationBox[
+ ButtonBox[
+ TooltipBox[
+ GraphicsBox[{{
+ GrayLevel[0],
+ RectangleBox[{0, 0}]}, {
+ GrayLevel[0],
+ RectangleBox[{1, -1}]}, {
+ RGBColor[0.560181, 0.691569, 0.194885],
+ RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle ->
+ "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True,
+ FrameStyle ->
+ RGBColor[
+ 0.37345400000000006`, 0.461046, 0.12992333333333334`],
+ FrameTicks -> None, PlotRangePadding -> None, ImageSize ->
+ Dynamic[{Automatic, 1.35 CurrentValue["FontCapHeight"]/
+ AbsoluteCurrentValue[Magnification]}]],
+ StyleBox[
+ RowBox[{"RGBColor", "[",
+ RowBox[{"0.560181`", ",", "0.691569`", ",", "0.194885`"}],
+ "]"}], NumberMarks -> False]], Appearance -> None,
+ BaseStyle -> {}, BaselinePosition -> Baseline,
+ DefaultBaseStyle -> {}, ButtonFunction :>
+ With[{Typeset`box$ = EvaluationBox[]},
+ If[
+ Not[
+ AbsoluteCurrentValue["Deployed"]],
+ SelectionMove[Typeset`box$, All, Expression];
+ FrontEnd`Private`$ColorSelectorInitialAlpha = 1;
+ FrontEnd`Private`$ColorSelectorInitialColor =
+ RGBColor[0.560181, 0.691569, 0.194885];
+ FrontEnd`Private`$ColorSelectorUseMakeBoxes = True;
+ MathLink`CallFrontEnd[
+ FrontEnd`AttachCell[Typeset`box$,
+ FrontEndResource["RGBColorValueSelector"], {
+ 0, {Left, Bottom}}, {Left, Top},
+ "ClosingActions" -> {
+ "SelectionDeparture", "ParentChanged",
+ "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator ->
+ Automatic, Method -> "Preemptive"],
+ RGBColor[0.560181, 0.691569, 0.194885], Editable -> False,
+ Selectable -> False], ",",
+ RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}],
+ "]"}]}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{#, ",", #2, ",", #3}], "}"}], ",",
+ RowBox[{"LegendMarkers", "\[Rule]", "None"}], ",",
+ RowBox[{"LabelStyle", "\[Rule]",
+ RowBox[{"{", "}"}]}], ",",
+ RowBox[{"LegendLayout", "\[Rule]", "\"Column\""}]}], "]"}]& ),
+ Editable -> True], TraditionalForm]}, {
+ FormBox[
+ TemplateBox[{"\"Re\"", "\"Im\"", "\"Abs\""}, "PointLegend",
+ DisplayFunction -> (StyleBox[
+ StyleBox[
+ PaneBox[
+ TagBox[
+ GridBox[{{
+ TagBox[
+ GridBox[{{
+ GraphicsBox[{{}, {
+ Directive[
+ EdgeForm[
+ Directive[
+ Opacity[0.3],
+ GrayLevel[0]]],
+ PointSize[0.5],
+ RGBColor[0.368417, 0.506779, 0.709798],
+ AbsoluteThickness[1.6]], {
+ Directive[
+ EdgeForm[
+ Directive[
+ Opacity[0.3],
+ GrayLevel[0]]],
+ PointSize[0.5],
+ RGBColor[0.368417, 0.506779, 0.709798],
+ AbsoluteThickness[1.6]],
+ PointBox[
+ NCache[{
+ Scaled[{
+ Rational[1, 2],
+ Rational[1, 2]}]}, {
+ Scaled[{0.5, 0.5}]}]]}}}, AspectRatio -> Full,
+ ImageSize -> {10, 10}, PlotRangePadding -> None,
+ ImagePadding -> Automatic,
+ BaselinePosition -> (Scaled[0.1] -> Baseline)], #}, {
+ GraphicsBox[{{}, {
+ Directive[
+ EdgeForm[
+ Directive[
+ Opacity[0.3],
+ GrayLevel[0]]],
+ PointSize[0.5],
+ RGBColor[0.880722, 0.611041, 0.142051],
+ AbsoluteThickness[1.6]], {
+ Directive[
+ EdgeForm[
+ Directive[
+ Opacity[0.3],
+ GrayLevel[0]]],
+ PointSize[0.5],
+ RGBColor[0.880722, 0.611041, 0.142051],
+ AbsoluteThickness[1.6]],
+ PointBox[
+ NCache[{
+ Scaled[{
+ Rational[1, 2],
+ Rational[1, 2]}]}, {
+ Scaled[{0.5, 0.5}]}]]}}}, AspectRatio -> Full,
+ ImageSize -> {10, 10}, PlotRangePadding -> None,
+ ImagePadding -> Automatic,
+ BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}, {
+ GraphicsBox[{{}, {
+ Directive[
+ EdgeForm[
+ Directive[
+ Opacity[0.3],
+ GrayLevel[0]]],
+ PointSize[0.5],
+ RGBColor[0.560181, 0.691569, 0.194885],
+ AbsoluteThickness[1.6]], {
+ Directive[
+ EdgeForm[
+ Directive[
+ Opacity[0.3],
+ GrayLevel[0]]],
+ PointSize[0.5],
+ RGBColor[0.560181, 0.691569, 0.194885],
+ AbsoluteThickness[1.6]],
+ PointBox[
+ NCache[{
+ Scaled[{
+ Rational[1, 2],
+ Rational[1, 2]}]}, {
+ Scaled[{0.5, 0.5}]}]]}}}, AspectRatio -> Full,
+ ImageSize -> {10, 10}, PlotRangePadding -> None,
+ ImagePadding -> Automatic,
+ BaselinePosition -> (Scaled[0.1] -> Baseline)], #3}},
+ GridBoxAlignment -> {
+ "Columns" -> {Center, Left}, "Rows" -> {{Baseline}}},
+ AutoDelete -> False,
+ GridBoxDividers -> {
+ "Columns" -> {{False}}, "Rows" -> {{False}}},
+ GridBoxItemSize -> {
+ "Columns" -> {{All}}, "Rows" -> {{All}}},
+ GridBoxSpacings -> {
+ "Columns" -> {{0.5}}, "Rows" -> {{0.8}}}], "Grid"]}},
+ GridBoxAlignment -> {
+ "Columns" -> {{Left}}, "Rows" -> {{Top}}}, AutoDelete ->
+ False, GridBoxItemSize -> {
+ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}},
+ GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}],
+ "Grid"], Alignment -> Left, AppearanceElements -> None,
+ ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction ->
+ "ResizeToFit"], LineIndent -> 0, StripOnInput -> False], {
+ FontFamily -> "Arial"}, Background -> Automatic, StripOnInput ->
+ False]& ),
+ InterpretationFunction :> (RowBox[{"PointLegend", "[",
+ RowBox[{
+ RowBox[{"{",
RowBox[{
- RowBox[{"PointSize", "[", "0.007333333333333334`", "]"}],
+ RowBox[{"Directive", "[",
+ RowBox[{
+ RowBox[{"PointSize", "[", "0.007333333333333334`", "]"}],
+ ",",
+ InterpretationBox[
+ ButtonBox[
+ TooltipBox[
+ GraphicsBox[{{
+ GrayLevel[0],
+ RectangleBox[{0, 0}]}, {
+ GrayLevel[0],
+ RectangleBox[{1, -1}]}, {
+ RGBColor[0.368417, 0.506779, 0.709798],
+ RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle ->
+ "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True,
+ FrameStyle ->
+ RGBColor[
+ 0.24561133333333335`, 0.3378526666666667,
+ 0.4731986666666667], FrameTicks -> None, PlotRangePadding ->
+ None, ImageSize ->
+ Dynamic[{Automatic, 1.35 CurrentValue["FontCapHeight"]/
+ AbsoluteCurrentValue[Magnification]}]],
+ StyleBox[
+ RowBox[{"RGBColor", "[",
+ RowBox[{"0.368417`", ",", "0.506779`", ",", "0.709798`"}],
+ "]"}], NumberMarks -> False]], Appearance -> None,
+ BaseStyle -> {}, BaselinePosition -> Baseline,
+ DefaultBaseStyle -> {}, ButtonFunction :>
+ With[{Typeset`box$ = EvaluationBox[]},
+ If[
+ Not[
+ AbsoluteCurrentValue["Deployed"]],
+ SelectionMove[Typeset`box$, All, Expression];
+ FrontEnd`Private`$ColorSelectorInitialAlpha = 1;
+ FrontEnd`Private`$ColorSelectorInitialColor =
+ RGBColor[0.368417, 0.506779, 0.709798];
+ FrontEnd`Private`$ColorSelectorUseMakeBoxes = True;
+ MathLink`CallFrontEnd[
+ FrontEnd`AttachCell[Typeset`box$,
+ FrontEndResource["RGBColorValueSelector"], {
+ 0, {Left, Bottom}}, {Left, Top},
+ "ClosingActions" -> {
+ "SelectionDeparture", "ParentChanged",
+ "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator ->
+ Automatic, Method -> "Preemptive"],
+ RGBColor[0.368417, 0.506779, 0.709798], Editable -> False,
+ Selectable -> False], ",",
+ RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}], "]"}],
",",
- InterpretationBox[
+ RowBox[{"Directive", "[",
+ RowBox[{
+ RowBox[{"PointSize", "[", "0.007333333333333334`", "]"}],
+ ",",
+ InterpretationBox[
+ ButtonBox[
+ TooltipBox[
+ GraphicsBox[{{
+ GrayLevel[0],
+ RectangleBox[{0, 0}]}, {
+ GrayLevel[0],
+ RectangleBox[{1, -1}]}, {
+ RGBColor[0.880722, 0.611041, 0.142051],
+ RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle ->
+ "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True,
+ FrameStyle ->
+ RGBColor[
+ 0.587148, 0.40736066666666665`, 0.09470066666666668],
+ FrameTicks -> None, PlotRangePadding -> None, ImageSize ->
+ Dynamic[{Automatic, 1.35 CurrentValue["FontCapHeight"]/
+ AbsoluteCurrentValue[Magnification]}]],
+ StyleBox[
+ RowBox[{"RGBColor", "[",
+ RowBox[{"0.880722`", ",", "0.611041`", ",", "0.142051`"}],
+ "]"}], NumberMarks -> False]], Appearance -> None,
+ BaseStyle -> {}, BaselinePosition -> Baseline,
+ DefaultBaseStyle -> {}, ButtonFunction :>
+ With[{Typeset`box$ = EvaluationBox[]},
+ If[
+ Not[
+ AbsoluteCurrentValue["Deployed"]],
+ SelectionMove[Typeset`box$, All, Expression];
+ FrontEnd`Private`$ColorSelectorInitialAlpha = 1;
+ FrontEnd`Private`$ColorSelectorInitialColor =
+ RGBColor[0.880722, 0.611041, 0.142051];
+ FrontEnd`Private`$ColorSelectorUseMakeBoxes = True;
+ MathLink`CallFrontEnd[
+ FrontEnd`AttachCell[Typeset`box$,
+ FrontEndResource["RGBColorValueSelector"], {
+ 0, {Left, Bottom}}, {Left, Top},
+ "ClosingActions" -> {
+ "SelectionDeparture", "ParentChanged",
+ "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator ->
+ Automatic, Method -> "Preemptive"],
+ RGBColor[0.880722, 0.611041, 0.142051], Editable -> False,
+ Selectable -> False], ",",
+ RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}], "]"}],
+ ",",
+ RowBox[{"Directive", "[",
+ RowBox[{
+ RowBox[{"PointSize", "[", "0.007333333333333334`", "]"}],
+ ",",
+ InterpretationBox[
ButtonBox[
TooltipBox[
GraphicsBox[{{
@@ -2318,8 +4132,7 @@ rCAgOoN6LhZ6uWosrXTqD6IqXFNaeeCKw3+A4dYQ
RGBColor[
0.37345400000000006`, 0.461046, 0.12992333333333334`],
FrameTicks -> None, PlotRangePadding -> None, ImageSize ->
- Dynamic[{
- Automatic, 1.35 CurrentValue["FontCapHeight"]/
+ Dynamic[{Automatic, 1.35 CurrentValue["FontCapHeight"]/
AbsoluteCurrentValue[Magnification]}]],
StyleBox[
RowBox[{"RGBColor", "[",
@@ -2346,26 +4159,32 @@ rCAgOoN6LhZ6uWosrXTqD6IqXFNaeeCKw3+A4dYQ
Automatic, Method -> "Preemptive"],
RGBColor[0.560181, 0.691569, 0.194885], Editable -> False,
Selectable -> False], ",",
- RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}], "]"}]}],
- "}"}], ",",
- RowBox[{"{",
- RowBox[{#, ",", #2, ",", #3}], "}"}], ",",
- RowBox[{"LegendMarkers", "\[Rule]",
- RowBox[{"{",
- RowBox[{
- RowBox[{"{",
- RowBox[{"False", ",", "Automatic"}], "}"}], ",",
+ RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}],
+ "]"}]}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{#, ",", #2, ",", #3}], "}"}], ",",
+ RowBox[{"LegendMarkers", "\[Rule]",
RowBox[{"{",
- RowBox[{"False", ",", "Automatic"}], "}"}], ",",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"False", ",", "Automatic"}], "}"}], ",",
+ RowBox[{"{",
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+ 0.4731986666666667], FrameTicks -> None, PlotRangePadding ->
+ None, ImageSize ->
+ Dynamic[{
+ Automatic, 1.35 CurrentValue["FontCapHeight"]/
+ AbsoluteCurrentValue[Magnification]}]],
+ StyleBox[
+ RowBox[{"RGBColor", "[",
+ RowBox[{"0.368417`", ",", "0.506779`", ",", "0.709798`"}],
+ "]"}], NumberMarks -> False]], Appearance -> None,
+ BaseStyle -> {}, BaselinePosition -> Baseline,
+ DefaultBaseStyle -> {}, ButtonFunction :>
+ With[{Typeset`box$ = EvaluationBox[]},
+ If[
+ Not[
+ AbsoluteCurrentValue["Deployed"]],
+ SelectionMove[Typeset`box$, All, Expression];
+ FrontEnd`Private`$ColorSelectorInitialAlpha = 1;
+ FrontEnd`Private`$ColorSelectorInitialColor =
+ RGBColor[0.368417, 0.506779, 0.709798];
+ FrontEnd`Private`$ColorSelectorUseMakeBoxes = True;
+ MathLink`CallFrontEnd[
+ FrontEnd`AttachCell[Typeset`box$,
+ FrontEndResource["RGBColorValueSelector"], {
+ 0, {Left, Bottom}}, {Left, Top},
+ "ClosingActions" -> {
+ "SelectionDeparture", "ParentChanged",
+ "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator ->
+ Automatic, Method -> "Preemptive"],
+ RGBColor[0.368417, 0.506779, 0.709798], Editable -> False,
+ Selectable -> False], ",",
+ RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}], "]"}],
+ "}"}], ",",
+ RowBox[{"{", #, "}"}], ",",
+ RowBox[{"LegendMarkers", "\[Rule]",
+ RowBox[{"{",
+ RowBox[{"{",
+ RowBox[{"False", ",", "Automatic"}], "}"}], "}"}]}], ",",
+
+ RowBox[{"Joined", "\[Rule]",
+ RowBox[{"{", "False", "}"}]}], ",",
+ RowBox[{"LabelStyle", "\[Rule]",
+ RowBox[{"{", "}"}]}], ",",
+ RowBox[{"LegendLayout", "\[Rule]", "\"Column\""}]}], "]"}]& ),
+ Editable -> True], TraditionalForm]}, {
+ FormBox[
+ TemplateBox[{"\"Analytical\""}, "LineLegend",
+ DisplayFunction -> (StyleBox[
+ StyleBox[
+ PaneBox[
+ TagBox[
+ GridBox[{{
+ TagBox[
+ GridBox[{{
+ GraphicsBox[{{
Directive[
EdgeForm[
Directive[
Opacity[0.3],
GrayLevel[0]]],
PointSize[0.5],
- RGBColor[0.880722, 0.611041, 0.142051],
+ Opacity[1.],
+ RGBColor[0.368417, 0.506779, 0.709798],
AbsoluteThickness[1.6]], {
LineBox[{{0, 10}, {20, 10}}]}}, {
Directive[
@@ -3045,59 +5047,281 @@ WtPjlHUDsNmfdmN+rQmZjwCw4+x7zBNM8B82c62a
Opacity[0.3],
GrayLevel[0]]],
PointSize[0.5],
- RGBColor[0.880722, 0.611041, 0.142051],
+ Opacity[1.],
+ RGBColor[0.368417, 0.506779, 0.709798],
AbsoluteThickness[1.6]], {}}}, AspectRatio -> Full,
ImageSize -> {20, 10}, PlotRangePadding -> None,
ImagePadding -> Automatic,
- BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}, {
- GraphicsBox[{{
+ BaselinePosition -> (Scaled[0.1] -> Baseline)], #}},
+ GridBoxAlignment -> {
+ "Columns" -> {Center, Left}, "Rows" -> {{Baseline}}},
+ AutoDelete -> False,
+ GridBoxDividers -> {
+ "Columns" -> {{False}}, "Rows" -> {{False}}},
+ GridBoxItemSize -> {
+ "Columns" -> {{All}}, "Rows" -> {{All}}},
+ GridBoxSpacings -> {
+ "Columns" -> {{0.5}}, "Rows" -> {{0.8}}}], "Grid"]}},
+ GridBoxAlignment -> {
+ "Columns" -> {{Left}}, "Rows" -> {{Top}}}, AutoDelete ->
+ False, GridBoxItemSize -> {
+ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}},
+ GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}],
+ "Grid"], Alignment -> Left, AppearanceElements -> None,
+ ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction ->
+ "ResizeToFit"], LineIndent -> 0, StripOnInput -> False], {
+ FontFamily -> "Arial"}, Background -> Automatic, StripOnInput ->
+ False]& ), InterpretationFunction :> (RowBox[{"LineLegend", "[",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"Directive", "[",
+ RowBox[{
+ RowBox[{"Opacity", "[", "1.`", "]"}], ",",
+ InterpretationBox[
+ ButtonBox[
+ TooltipBox[
+ GraphicsBox[{{
+ GrayLevel[0],
+ RectangleBox[{0, 0}]}, {
+ GrayLevel[0],
+ RectangleBox[{1, -1}]}, {
+ RGBColor[0.368417, 0.506779, 0.709798],
+ RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle ->
+ "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True,
+ FrameStyle ->
+ RGBColor[
+ 0.24561133333333335`, 0.3378526666666667,
+ 0.4731986666666667], FrameTicks -> None, PlotRangePadding ->
+ None, ImageSize ->
+ Dynamic[{
+ Automatic, 1.35 CurrentValue["FontCapHeight"]/
+ AbsoluteCurrentValue[Magnification]}]],
+ StyleBox[
+ RowBox[{"RGBColor", "[",
+ RowBox[{"0.368417`", ",", "0.506779`", ",", "0.709798`"}],
+ "]"}], NumberMarks -> False]], Appearance -> None,
+ BaseStyle -> {}, BaselinePosition -> Baseline,
+ DefaultBaseStyle -> {}, ButtonFunction :>
+ With[{Typeset`box$ = EvaluationBox[]},
+ If[
+ Not[
+ AbsoluteCurrentValue["Deployed"]],
+ SelectionMove[Typeset`box$, All, Expression];
+ FrontEnd`Private`$ColorSelectorInitialAlpha = 1;
+ FrontEnd`Private`$ColorSelectorInitialColor =
+ RGBColor[0.368417, 0.506779, 0.709798];
+ FrontEnd`Private`$ColorSelectorUseMakeBoxes = True;
+ MathLink`CallFrontEnd[
+ FrontEnd`AttachCell[Typeset`box$,
+ FrontEndResource["RGBColorValueSelector"], {
+ 0, {Left, Bottom}}, {Left, Top},
+ "ClosingActions" -> {
+ "SelectionDeparture", "ParentChanged",
+ "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator ->
+ Automatic, Method -> "Preemptive"],
+ RGBColor[0.368417, 0.506779, 0.709798], Editable -> False,
+ Selectable -> False], ",",
+ RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}], "]"}],
+ "}"}], ",",
+ RowBox[{"{", #, "}"}], ",",
+ RowBox[{"LegendMarkers", "\[Rule]", "None"}], ",",
+ RowBox[{"LabelStyle", "\[Rule]",
+ RowBox[{"{", "}"}]}], ",",
+ RowBox[{"LegendLayout", "\[Rule]", "\"Column\""}]}], "]"}]& ),
+ Editable -> True], TraditionalForm]}},
+ GridBoxAlignment -> {"Columns" -> {{Left}}}, AutoDelete -> False,
+ GridBoxItemSize -> {
+ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}},
+ GridBoxSpacings -> {"Columns" -> {{0}}}], "Grid"], TraditionalForm]},
+ "Legended",
+ DisplayFunction->(GridBox[{{
+ TagBox[
+ ItemBox[
+ PaneBox[
+ TagBox[#, "SkipImageSizeLevel"], Alignment -> {Center, Baseline},
+ BaselinePosition -> Baseline], DefaultBaseStyle -> "Labeled"],
+ "SkipImageSizeLevel"],
+ ItemBox[#2, DefaultBaseStyle -> "LabeledLabel"]}},
+ GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}},
+ AutoDelete -> False, GridBoxItemSize -> Automatic,
+ BaselinePosition -> {1, 1}]& ),
+ Editable->True,
+ InterpretationFunction->(RowBox[{"Legended", "[",
+ RowBox[{#, ",",
+ RowBox[{"Placed", "[",
+ RowBox[{#2, ",", "After"}], "]"}]}], "]"}]& )]], "Output",
+ CellChangeTimes->{{3.874745759583666*^9, 3.874745784036532*^9}, {
+ 3.874745824047166*^9, 3.87474585740758*^9}, 3.874748249177383*^9,
+ 3.874748657867485*^9, 3.874749333113696*^9},
+ CellLabel->
+ "Out[313]=",ExpressionUUID->"2944f73b-3f5c-4df0-815b-ce8a2290a95b"],
+
+Cell[BoxData[
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+ ImageSize -> 250, DisplayFunction -> Identity, DisplayFunction ->
+ Identity, AspectRatio -> NCache[GoldenRatio^(-1), 0.6180339887498948],
+ Axes -> {True, True}, AxesLabel -> {None, None}, AxesOrigin -> {0, 0},
+ DisplayFunction :> Identity, Frame -> {{False, False}, {False, False}},
+ FrameLabel -> {{None, None}, {None, None}},
+ FrameTicks -> {{Automatic, Automatic}, {Automatic, Automatic}},
+ GridLines -> {None, None}, GridLinesStyle -> Directive[
+ GrayLevel[0.5, 0.4]],
+ Method -> {
+ "OptimizePlotMarkers" -> True,
+ "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
+ (Identity[#]& )[
+ Part[#, 1]],
+ (Identity[#]& )[
+ Part[#, 2]]}& ), "CopiedValueFunction" -> ({
+ (Identity[#]& )[
+ Part[#, 1]],
+ (Identity[#]& )[
+ Part[#, 2]]}& )}}, PlotLabel ->
+ FormBox["\"Im\"", TraditionalForm],
+ PlotRange -> {{0, 100.}, {0, 56.999616591307}}, PlotRangeClipping ->
+ True, PlotRangePadding -> {{
+ Scaled[0.02],
+ Scaled[0.02]}, {
+ Scaled[0.02],
+ Scaled[0.05]}}, Ticks -> {Automatic, Automatic}}],FormBox[
+ TagBox[
+ GridBox[{{
+ FormBox[
+ TemplateBox[{"\"Numerical\""}, "PointLegend",
+ DisplayFunction -> (StyleBox[
+ StyleBox[
+ PaneBox[
+ TagBox[
+ GridBox[{{
+ TagBox[
+ GridBox[{{
+ GraphicsBox[{{}, {
Directive[
EdgeForm[
Directive[
Opacity[0.3],
GrayLevel[0]]],
PointSize[0.5],
- RGBColor[0.560181, 0.691569, 0.194885],
+ RGBColor[0.368417, 0.506779, 0.709798],
AbsoluteThickness[1.6]], {
- LineBox[{{0, 10}, {20, 10}}]}}, {
Directive[
EdgeForm[
Directive[
Opacity[0.3],
GrayLevel[0]]],
PointSize[0.5],
- RGBColor[0.560181, 0.691569, 0.194885],
- AbsoluteThickness[1.6]], {}}}, AspectRatio -> Full,
- ImageSize -> {20, 10}, PlotRangePadding -> None,
+ RGBColor[0.368417, 0.506779, 0.709798],
+ AbsoluteThickness[1.6]],
+ PointBox[
+ NCache[{
+ Scaled[{
+ Rational[1, 2],
+ Rational[1, 2]}]}, {
+ Scaled[{0.5, 0.5}]}]]}}}, AspectRatio -> Full,
+ ImageSize -> {10, 10}, PlotRangePadding -> None,
ImagePadding -> Automatic,
- BaselinePosition -> (Scaled[0.1] -> Baseline)], #3}},
- GridBoxAlignment -> {
- "Columns" -> {Center, Left}, "Rows" -> {{Baseline}}},
- AutoDelete -> False,
- GridBoxDividers -> {
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- GridBoxItemSize -> {"Columns" -> {{All}}, "Rows" -> {{All}}},
- GridBoxSpacings -> {
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- GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}},
- AutoDelete -> False,
- GridBoxItemSize -> {
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- GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}],
- "Grid"], Alignment -> Left, AppearanceElements -> None,
- ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction ->
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- FontFamily -> "Arial"}, Background -> Automatic, StripOnInput ->
- False], TraditionalForm]& ),
- InterpretationFunction :> (RowBox[{"PointLegend", "[",
- RowBox[{
- RowBox[{"{",
+ BaselinePosition -> (Scaled[0.1] -> Baseline)], #}},
+ GridBoxAlignment -> {
+ "Columns" -> {Center, Left}, "Rows" -> {{Baseline}}},
+ AutoDelete -> False,
+ GridBoxDividers -> {
+ "Columns" -> {{False}}, "Rows" -> {{False}}},
+ GridBoxItemSize -> {
+ "Columns" -> {{All}}, "Rows" -> {{All}}},
+ GridBoxSpacings -> {
+ "Columns" -> {{0.5}}, "Rows" -> {{0.8}}}], "Grid"]}},
+ GridBoxAlignment -> {
+ "Columns" -> {{Left}}, "Rows" -> {{Top}}}, AutoDelete ->
+ False, GridBoxItemSize -> {
+ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}},
+ GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}],
+ "Grid"], Alignment -> Left, AppearanceElements -> None,
+ ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction ->
+ "ResizeToFit"], LineIndent -> 0, StripOnInput -> False], {
+ FontFamily -> "Arial"}, Background -> Automatic, StripOnInput ->
+ False]& ),
+ InterpretationFunction :> (RowBox[{"PointLegend", "[",
RowBox[{
- RowBox[{"Directive", "[",
- RowBox[{
- RowBox[{"PointSize", "[", "0.007333333333333334`", "]"}],
- ",",
- InterpretationBox[
+ RowBox[{"{",
+ RowBox[{"Directive", "[",
+ RowBox[{
+ RowBox[{"PointSize", "[", "0.009166666666666668`", "]"}],
+ ",",
+ InterpretationBox[
ButtonBox[
TooltipBox[
GraphicsBox[{{
@@ -3141,62 +5365,77 @@ WtPjlHUDsNmfdmN+rQmZjwCw4+x7zBNM8B82c62a
Automatic, Method -> "Preemptive"],
RGBColor[0.368417, 0.506779, 0.709798], Editable -> False,
Selectable -> False], ",",
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- ",",
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- RowBox[{
- RowBox[{"PointSize", "[", "0.007333333333333334`", "]"}],
- ",",
- InterpretationBox[
- ButtonBox[
- TooltipBox[
+ RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}], "]"}],
+ "}"}], ",",
+ RowBox[{"{", #, "}"}], ",",
+ RowBox[{"LegendMarkers", "\[Rule]",
+ RowBox[{"{",
+ RowBox[{"{",
+ RowBox[{"False", ",", "Automatic"}], "}"}], "}"}]}], ",",
+
+ RowBox[{"Joined", "\[Rule]",
+ RowBox[{"{", "False", "}"}]}], ",",
+ RowBox[{"LabelStyle", "\[Rule]",
+ RowBox[{"{", "}"}]}], ",",
+ RowBox[{"LegendLayout", "\[Rule]", "\"Column\""}]}], "]"}]& ),
+ Editable -> True], TraditionalForm]}, {
+ FormBox[
+ TemplateBox[{"\"Analytical\""}, "LineLegend",
+ DisplayFunction -> (StyleBox[
+ StyleBox[
+ PaneBox[
+ TagBox[
+ GridBox[{{
+ TagBox[
+ GridBox[{{
GraphicsBox[{{
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- RectangleBox[{0, 0}]}, {
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- RectangleBox[{1, -1}]}, {
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- FrameStyle ->
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- FrameTicks -> None, PlotRangePadding -> None, ImageSize ->
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- StyleBox[
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- BaseStyle -> {}, BaselinePosition -> Baseline,
- DefaultBaseStyle -> {}, ButtonFunction :>
- With[{Typeset`box$ = EvaluationBox[]},
- If[
- Not[
- AbsoluteCurrentValue["Deployed"]],
- SelectionMove[Typeset`box$, All, Expression];
- FrontEnd`Private`$ColorSelectorInitialAlpha = 1;
- FrontEnd`Private`$ColorSelectorInitialColor =
- RGBColor[0.880722, 0.611041, 0.142051];
- FrontEnd`Private`$ColorSelectorUseMakeBoxes = True;
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Evaluator -> Automatic, Method -> "Preemptive"],
Alignment -> {Center, Center}, ImageSize ->
Dynamic[{
- Automatic, 3.5 CurrentValue["FontCapHeight"]/
- AbsoluteCurrentValue[Magnification]}]],
+ Automatic,
+ 3.5 (CurrentValue["FontCapHeight"]/AbsoluteCurrentValue[
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GraphicsBox[{{
GrayLevel[0.6],
AbsolutePointSize[5],
@@ -239529,8 +241983,9 @@ q5SZmRFAL++xNeOlE0Dwt3AR
Evaluator -> Automatic, Method -> "Preemptive"],
Alignment -> {Center, Center}, ImageSize ->
Dynamic[{
- Automatic, 3.5 CurrentValue["FontCapHeight"]/
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Evaluator -> Automatic, Method -> "Preemptive"],
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Dynamic[{
- Automatic, 3.5 CurrentValue["FontCapHeight"]/
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+ FrontEnd`Private`$ColorSelectorUseMakeBoxes = True;
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+ BaseStyle -> {}, BaselinePosition -> Baseline,
+ DefaultBaseStyle -> {}, ButtonFunction :>
+ With[{Typeset`box$ = EvaluationBox[]},
+ If[
+ Not[
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+ SelectionMove[Typeset`box$, All, Expression];
+ FrontEnd`Private`$ColorSelectorInitialAlpha = 1;
+ FrontEnd`Private`$ColorSelectorInitialColor =
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+ FrontEnd`Private`$ColorSelectorUseMakeBoxes = True;
+ MathLink`CallFrontEnd[
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+ "ClosingActions" -> {
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+ FrameStyle ->
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+ GridBoxDividers -> {
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+ GridBoxSpacings -> {
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+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"Directive", "[",
+ RowBox[{
+ RowBox[{"Opacity", "[", "1.`", "]"}], ",",
+ InterpretationBox[
+ ButtonBox[
+ TooltipBox[
+ GraphicsBox[{{
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+ RectangleBox[{0, 0}]}, {
+ GrayLevel[0],
+ RectangleBox[{1, -1}]}, {
+ RGBColor[0.368417, 0.506779, 0.709798],
+ RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle ->
+ "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True,
+ FrameStyle -> RGBColor[
+ 0.24561133333333335`, 0.3378526666666667,
+ 0.4731986666666667], FrameTicks -> None, PlotRangePadding ->
+ None, ImageSize ->
+ Dynamic[{Automatic, 1.35 CurrentValue["FontCapHeight"]/
+ AbsoluteCurrentValue[Magnification]}]],
+ StyleBox[
+ RowBox[{"RGBColor", "[",
+ RowBox[{"0.368417`", ",", "0.506779`", ",", "0.709798`"}],
+ "]"}], NumberMarks -> False]], Appearance -> None,
+ BaseStyle -> {}, BaselinePosition -> Baseline,
+ DefaultBaseStyle -> {}, ButtonFunction :>
+ With[{Typeset`box$ = EvaluationBox[]},
+ If[
+ Not[
+ AbsoluteCurrentValue["Deployed"]],
+ SelectionMove[Typeset`box$, All, Expression];
+ FrontEnd`Private`$ColorSelectorInitialAlpha = 1;
+ FrontEnd`Private`$ColorSelectorInitialColor =
+ RGBColor[0.368417, 0.506779, 0.709798];
+ FrontEnd`Private`$ColorSelectorUseMakeBoxes = True;
+ MathLink`CallFrontEnd[
+ FrontEnd`AttachCell[Typeset`box$,
+ FrontEndResource["RGBColorValueSelector"], {
+ 0, {Left, Bottom}}, {Left, Top},
+ "ClosingActions" -> {
+ "SelectionDeparture", "ParentChanged",
+ "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator ->
+ Automatic, Method -> "Preemptive"],
+ RGBColor[0.368417, 0.506779, 0.709798], Editable -> False,
+ Selectable -> False], ",",
+ RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}], "]"}],
+ ",",
+ RowBox[{"Directive", "[",
+ RowBox[{
+ RowBox[{"Opacity", "[", "1.`", "]"}], ",",
+ InterpretationBox[
ButtonBox[
TooltipBox[
GraphicsBox[{{
@@ -246026,20 +250570,17 @@ rLuTtKZAACa4VuAlXiipqDxhb6soAOXLS93d04+Sqq3hJfFKor7mp0Ep5PmQ
RectangleBox[{0, 0}]}, {
GrayLevel[0],
RectangleBox[{1, -1}]}, {
- RGBColor[0.368417, 0.506779, 0.709798],
+ RGBColor[0.880722, 0.611041, 0.142051],
RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle ->
"ColorSwatchGraphics", AspectRatio -> 1, Frame -> True,
- FrameStyle ->
- RGBColor[
- 0.24561133333333335`, 0.3378526666666667,
- 0.4731986666666667], FrameTicks -> None, PlotRangePadding ->
- None, ImageSize ->
- Dynamic[{
- Automatic, 1.35 CurrentValue["FontCapHeight"]/
+ FrameStyle -> RGBColor[
+ 0.587148, 0.40736066666666665`, 0.09470066666666668],
+ FrameTicks -> None, PlotRangePadding -> None, ImageSize ->
+ Dynamic[{Automatic, 1.35 CurrentValue["FontCapHeight"]/
AbsoluteCurrentValue[Magnification]}]],
StyleBox[
RowBox[{"RGBColor", "[",
- RowBox[{"0.368417`", ",", "0.506779`", ",", "0.709798`"}],
+ RowBox[{"0.880722`", ",", "0.611041`", ",", "0.142051`"}],
"]"}], NumberMarks -> False]], Appearance -> None,
BaseStyle -> {}, BaselinePosition -> Baseline,
DefaultBaseStyle -> {}, ButtonFunction :>
@@ -246050,7 +250591,7 @@ rLuTtKZAACa4VuAlXiipqDxhb6soAOXLS93d04+Sqq3hJfFKor7mp0Ep5PmQ
SelectionMove[Typeset`box$, All, Expression];
FrontEnd`Private`$ColorSelectorInitialAlpha = 1;
FrontEnd`Private`$ColorSelectorInitialColor =
- RGBColor[0.368417, 0.506779, 0.709798];
+ RGBColor[0.880722, 0.611041, 0.142051];
FrontEnd`Private`$ColorSelectorUseMakeBoxes = True;
MathLink`CallFrontEnd[
FrontEnd`AttachCell[Typeset`box$,
@@ -246060,16 +250601,167 @@ rLuTtKZAACa4VuAlXiipqDxhb6soAOXLS93d04+Sqq3hJfFKor7mp0Ep5PmQ
"SelectionDeparture", "ParentChanged",
"EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator ->
Automatic, Method -> "Preemptive"],
- RGBColor[0.368417, 0.506779, 0.709798], Editable -> False,
+ RGBColor[0.880722, 0.611041, 0.142051], Editable -> False,
Selectable -> False], ",",
- RowBox[{"Dashing", "[",
- RowBox[{"{",
- RowBox[{"Small", ",", "Small"}], "}"}], "]"}]}], "]"}],
- ",",
+ RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}],
+ "]"}]}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{#, ",", #2}], "}"}], ",",
+ RowBox[{"LegendMarkers", "\[Rule]", "None"}], ",",
+ RowBox[{"LabelStyle", "\[Rule]",
+ RowBox[{"{", "}"}]}], ",",
+ RowBox[{"LegendLayout", "\[Rule]", "\"Column\""}]}],
+ "]"}]& ), Editable -> True], TraditionalForm],
+ TraditionalForm]}, "Legended", DisplayFunction -> (FormBox[
+ GridBox[{{
+ ItemBox[#2, DefaultBaseStyle -> "LabeledLabel"],
+ TagBox[
+ ItemBox[
+ PaneBox[
+ TagBox[#, "SkipImageSizeLevel"],
+ Alignment -> {Center, Baseline}, BaselinePosition ->
+ Baseline], DefaultBaseStyle -> "Labeled"],
+ "SkipImageSizeLevel"]}},
+ GridBoxAlignment -> {
+ "Columns" -> {{Center}}, "Rows" -> {{Center}}}, AutoDelete ->
+ False, GridBoxItemSize -> Automatic, BaselinePosition -> {1, 2}],
+ TraditionalForm]& ), InterpretationFunction -> (FormBox[
+ RowBox[{"Legended", "(",
+ RowBox[{#, ",",
+ RowBox[{"Placed", "[",
+ RowBox[{#2, ",", "Before"}], "]"}]}], ")"}],
+ TraditionalForm]& ), Editable -> True], TraditionalForm]], {0.91,
+ 0.12}, {0.5, 0.5}, 0.45], ImageSize -> 400, DisplayFunction ->
+ Identity, Ticks -> {Automatic, Automatic},
+ AxesOrigin -> {0.5, 0.11501792774717608`}, FrameTicks -> {{Automatic,
+ Charting`ScaledFrameTicks[{Identity, Identity}]}, {Automatic,
+ Charting`ScaledFrameTicks[{Identity, Identity}]}},
+ GridLines -> {None, None}, DisplayFunction -> Identity,
+ PlotRangePadding -> {{
+ Scaled[0.02],
+ Scaled[0.02]}, {
+ Scaled[0.05],
+ Scaled[0.05]}}, PlotRangeClipping -> True, ImagePadding -> All,
+ DisplayFunction -> Identity, AspectRatio ->
+ NCache[GoldenRatio^(-1), 0.6180339887498948], Axes -> {True, True},
+ AxesLabel -> {None, None}, AxesOrigin -> {0.5, 0.11501792774717608`},
+ DisplayFunction :> Identity, Frame -> {{False, False}, {False, False}},
+ FrameLabel -> {{None, None}, {None, None}},
+ FrameTicks -> {{Automatic, Automatic}, {Automatic, Automatic}},
+ GridLines -> {None, None}, GridLinesStyle -> Directive[
+ GrayLevel[0.5, 0.4]],
+ Method -> {
+ "DefaultBoundaryStyle" -> Automatic,
+ "DefaultGraphicsInteraction" -> {
+ "Version" -> 1.2, "TrackMousePosition" -> {True, False},
+ "Effects" -> {
+ "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2},
+ "Droplines" -> {
+ "freeformCursorMode" -> True,
+ "placement" -> {"x" -> "All", "y" -> "None"}}}},
+ "DefaultMeshStyle" -> AbsolutePointSize[6], "ScalingFunctions" -> None,
+ "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
+ (Identity[#]& )[
+ Part[#, 1]],
+ (Identity[#]& )[
+ Part[#, 2]]}& ), "CopiedValueFunction" -> ({
+ (Identity[#]& )[
+ Part[#, 1]],
+ (Identity[#]& )[
+ Part[#, 2]]}& )}},
+ PlotRange -> {{0.5, 1}, {0.11501792774717608`, 0.23003584948632802`}},
+ PlotRangeClipping -> True, PlotRangePadding -> {{
+ Scaled[0.02],
+ Scaled[0.02]}, {
+ Scaled[0.02],
+ Scaled[0.02]}}, Ticks -> {Automatic, Automatic}}],FormBox[
+ FormBox[
+ TemplateBox[{
+ "\"\\!\\(\\*FractionBox[\\(1\\), SuperscriptBox[\\(\[Pi]\\), \
+\\(2\\)]]\\)(K[\\!\\(\\*SubscriptBox[\\(\[Gamma]\\), \
+\\(E\\)]\\)+log(2\\!\\(\\*SubscriptBox[\\(v\\), \\(F\\)]\\))]+1)\"",
+ "\"\\!\\(\\*FractionBox[\\(1\\), SuperscriptBox[\\(\[Pi]\\), \\(2\\)]]\
+\\)K[\\!\\(\\*SubscriptBox[\\(\[Gamma]\\), \
+\\(E\\)]\\)+log(2\\!\\(\\*SubscriptBox[\\(v\\), \\(F\\)]\\))+1]\""},
+ "LineLegend", DisplayFunction -> (FormBox[
+ StyleBox[
+ StyleBox[
+ PaneBox[
+ TagBox[
+ GridBox[{{
+ TagBox[
+ GridBox[{{
+ GraphicsBox[{{
+ Directive[
+ EdgeForm[
+ Directive[
+ Opacity[0.3],
+ GrayLevel[0]]],
+ PointSize[0.5],
+ Opacity[1.],
+ RGBColor[0.368417, 0.506779, 0.709798],
+ AbsoluteThickness[1.6]], {
+ LineBox[{{0, 10}, {20, 10}}]}}, {
+ Directive[
+ EdgeForm[
+ Directive[
+ Opacity[0.3],
+ GrayLevel[0]]],
+ PointSize[0.5],
+ Opacity[1.],
+ RGBColor[0.368417, 0.506779, 0.709798],
+ AbsoluteThickness[1.6]], {}}}, AspectRatio -> Full,
+ ImageSize -> {20, 10}, PlotRangePadding -> None,
+ ImagePadding -> Automatic,
+ BaselinePosition -> (Scaled[0.1] -> Baseline)], #}, {
+ GraphicsBox[{{
+ Directive[
+ EdgeForm[
+ Directive[
+ Opacity[0.3],
+ GrayLevel[0]]],
+ PointSize[0.5],
+ Opacity[1.],
+ RGBColor[0.880722, 0.611041, 0.142051],
+ AbsoluteThickness[1.6]], {
+ LineBox[{{0, 10}, {20, 10}}]}}, {
+ Directive[
+ EdgeForm[
+ Directive[
+ Opacity[0.3],
+ GrayLevel[0]]],
+ PointSize[0.5],
+ Opacity[1.],
+ RGBColor[0.880722, 0.611041, 0.142051],
+ AbsoluteThickness[1.6]], {}}}, AspectRatio -> Full,
+ ImageSize -> {20, 10}, PlotRangePadding -> None,
+ ImagePadding -> Automatic,
+ BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}},
+ GridBoxAlignment -> {
+ "Columns" -> {Center, Left}, "Rows" -> {{Baseline}}},
+ AutoDelete -> False,
+ GridBoxDividers -> {
+ "Columns" -> {{False}}, "Rows" -> {{False}}},
+ GridBoxItemSize -> {"Columns" -> {{All}}, "Rows" -> {{All}}},
+ GridBoxSpacings -> {
+ "Columns" -> {{0.5}}, "Rows" -> {{0.8}}}], "Grid"]}},
+ GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}},
+ AutoDelete -> False,
+ GridBoxItemSize -> {
+ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}},
+ GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}],
+ "Grid"], Alignment -> Left, AppearanceElements -> None,
+ ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction ->
+ "ResizeToFit"], LineIndent -> 0, StripOnInput -> False], {
+ FontFamily -> "Arial"}, Background -> Automatic, StripOnInput ->
+ False], TraditionalForm]& ),
+ InterpretationFunction :> (RowBox[{"LineLegend", "[",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{
RowBox[{"Directive", "[",
RowBox[{
RowBox[{"Opacity", "[", "1.`", "]"}], ",",
- RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",",
InterpretationBox[
ButtonBox[
TooltipBox[
@@ -246078,19 +250770,20 @@ rLuTtKZAACa4VuAlXiipqDxhb6soAOXLS93d04+Sqq3hJfFKor7mp0Ep5PmQ
RectangleBox[{0, 0}]}, {
GrayLevel[0],
RectangleBox[{1, -1}]}, {
- RGBColor[0.880722, 0.611041, 0.142051],
+ RGBColor[0.368417, 0.506779, 0.709798],
RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle ->
"ColorSwatchGraphics", AspectRatio -> 1, Frame -> True,
FrameStyle ->
RGBColor[
- 0.587148, 0.40736066666666665`, 0.09470066666666668],
- FrameTicks -> None, PlotRangePadding -> None, ImageSize ->
+ 0.24561133333333335`, 0.3378526666666667,
+ 0.4731986666666667], FrameTicks -> None, PlotRangePadding ->
+ None, ImageSize ->
Dynamic[{
Automatic, 1.35 CurrentValue["FontCapHeight"]/
AbsoluteCurrentValue[Magnification]}]],
StyleBox[
RowBox[{"RGBColor", "[",
- RowBox[{"0.880722`", ",", "0.611041`", ",", "0.142051`"}],
+ RowBox[{"0.368417`", ",", "0.506779`", ",", "0.709798`"}],
"]"}], NumberMarks -> False]], Appearance -> None,
BaseStyle -> {}, BaselinePosition -> Baseline,
DefaultBaseStyle -> {}, ButtonFunction :>
@@ -246101,7 +250794,7 @@ rLuTtKZAACa4VuAlXiipqDxhb6soAOXLS93d04+Sqq3hJfFKor7mp0Ep5PmQ
SelectionMove[Typeset`box$, All, Expression];
FrontEnd`Private`$ColorSelectorInitialAlpha = 1;
FrontEnd`Private`$ColorSelectorInitialColor =
- RGBColor[0.880722, 0.611041, 0.142051];
+ RGBColor[0.368417, 0.506779, 0.709798];
FrontEnd`Private`$ColorSelectorUseMakeBoxes = True;
MathLink`CallFrontEnd[
FrontEnd`AttachCell[Typeset`box$,
@@ -246111,12 +250804,13 @@ rLuTtKZAACa4VuAlXiipqDxhb6soAOXLS93d04+Sqq3hJfFKor7mp0Ep5PmQ
"SelectionDeparture", "ParentChanged",
"EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator ->
Automatic, Method -> "Preemptive"],
- RGBColor[0.880722, 0.611041, 0.142051], Editable -> False,
- Selectable -> False]}], "]"}], ",",
+ RGBColor[0.368417, 0.506779, 0.709798], Editable -> False,
+ Selectable -> False], ",",
+ RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}], "]"}],
+ ",",
RowBox[{"Directive", "[",
RowBox[{
RowBox[{"Opacity", "[", "1.`", "]"}], ",",
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InterpretationBox[
ButtonBox[
TooltipBox[
@@ -246160,12 +250854,10 @@ rLuTtKZAACa4VuAlXiipqDxhb6soAOXLS93d04+Sqq3hJfFKor7mp0Ep5PmQ
Automatic, Method -> "Preemptive"],
RGBColor[0.880722, 0.611041, 0.142051], Editable -> False,
Selectable -> False], ",",
- RowBox[{"Dashing", "[",
- RowBox[{"{",
- RowBox[{"Small", ",", "Small"}], "}"}], "]"}]}], "]"}]}],
- "}"}], ",",
+ RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}], "]"}]}],
+ "}"}], ",",
RowBox[{"{",
- RowBox[{#, ",", #2, ",", #3, ",", #4}], "}"}], ",",
+ RowBox[{#, ",", #2}], "}"}], ",",
RowBox[{"LegendMarkers", "\[Rule]", "None"}], ",",
RowBox[{"LabelStyle", "\[Rule]",
RowBox[{"{", "}"}]}], ",",
@@ -246188,95 +250880,37 @@ rLuTtKZAACa4VuAlXiipqDxhb6soAOXLS93d04+Sqq3hJfFKor7mp0Ep5PmQ
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}, Open ]]
},
WindowSize->{1192, 769},
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+WindowMargins->{{0, Automatic}, {10, Automatic}},
FrontEndVersion->"12.0 for Mac OS X x86 (64-bit) (April 8, 2019)",
StyleDefinitions->"Default.nb"
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@@ -246289,13 +250923,13 @@ CellTagsIndex->{
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CellTags->"init"]}
}
*)
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CellTagsIndex->{
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diff --git a/determinant.tex b/determinant.tex
index ddf80df5a6fb04996940d4e710643c34d2b79d2f..0b6557ed3a7e33b49ff7e09d40df39fb00d5c89b 100644
--- a/determinant.tex
+++ b/determinant.tex
@@ -17,9 +17,9 @@
%\def\fileversion{\InputIfFileExists{.git/current_version}{\it version~}{\it unversioned}%
-\def\fileversion{\it version~0.4\,%
+\def\fileversion{\it version~1.1\,%
%(\pdffilesize{\jobname.tex} bytes)}
-\if\pdfstrcmp{\pdffilesize{\jobname.tex}}{18119}0{(original)}\else{(changed)}\fi}
+\if\pdfstrcmp{\pdffilesize{\jobname.tex}}{21446}0{(original)}\else{(changed)}\fi}
\DeclareMathOperator{\Tr}{Tr}
\DeclareGraphicsExtensions{.pdf,.ai}
@@ -41,7 +41,7 @@
\maketitle
-{\parskip-\baselineskip\par\noindent {\hfill\raisebox{-\baselineskip}[0pt][0pt]{\fileversion}\hfill}}
+{\parskip-\baselineskip\par\noindent {\hfill\raisebox{-\baselineskip}[0pt][10pt]{\fileversion}\hfill}}
@@ -457,11 +457,78 @@ In this case the solution is easy and equal
x_{0} = \left(1+\gamma c + \frac{i}{\pi} \gamma \log\frac{1-e^{i\pi c}}{1-e^{-i\pi c}} \right)^{-1}
\end{equation}
-\section{Hubbart-Stratanovich with auxiliary fermionic field}
+%\section{Hubbart-Stratanovich with auxiliary fermionic field}
+%
+%\begin{equation}
+%\mathrm{Tr}_{d} \left[e^{i \lambda d^{+} d} e^{i \frac{\pi}{2} (d^{+} a + a^{+} d)}\right] = e^{i\lambda a^{+}a}
+%\end{equation}
+
+
+%\section{The finite temperature case}
+%
+%For finite temperature the function $f(e^{i\theta})$ is analytic:
+%\begin{multline}
+%-\log f(e^{i\theta}) = -\log \frac{1}{e^{2\beta\cos\theta - \alpha}} =
+%\sum_{n=1}^{\infty}\frac{1}{n}e^{-\alpha n} e^{2n\beta\cos\theta} =
+%\sum_{n=1}^{\infty}\frac{e^{-\alpha n}}{n}\sum_{m=0}^{\infty} \frac{n^{m}\beta^{m}}{m!} (2\cos\theta)^{m}
+%=\\=
+%\sum_{n=1}^{\infty}\frac{e^{-\alpha n}}{n}\sum_{m=0}^{\infty} \frac{n^{m}\beta^{m}}{m!} \sum_{k=0}^{m} C^{k}_{m} e^{i(2k-m)\theta}
+%=
+%\sum_{n=1}^{\infty}\frac{e^{-\alpha n}}{n}\sum_{m=0}^{\infty} \sum_{k=0}^{m} \frac{n^{m}\beta^{m}}{k!(m-k)!} e^{i(2k-m)\theta}
+%\end{multline}
+%so that for $\log f(z)=\sum_{l=-\infty}^{\infty}V_{l} z^{l} $ we get
+%\begin{equation}
+%V_{l} = \sum_{n=1}^{\infty}\sum_{s=0}^{\infty} \frac{n^{|l|+2s-1}\beta^{|l|+2s}e^{-\alpha n}}{s!(|l|+s)!}
+%=\sum_{n=1}\frac{e^{-\alpha n}}{n}I_{l}(2\beta n)
+%\end{equation}
+%where $I_{l}(z)$ is modified Bessel function of the first kind.
+
+
+\section{The logarithmic term in Szeg\"o theorem}
+
+Let us consider more accurately the Fisher-Hartwig formula.
+We follow the designations given in \cite{Deift2011} and \cite{Abanov2011}
+In our case
+\begin{equation}
+f(e^{i\theta}) = 1 + (e^{i\lambda}-1)\frac{1}{e^{2\beta\cos\theta - \alpha}+1}
+\end{equation}
+It is crucial to be able to expand into Laurent series:
+\begin{equation}
+\log f(z) = \sum_{l=-\infty}^{\infty}V_{l}z^{l}
+\end{equation}
+For finite $\beta$ the $V_{l}$ gets a cutoff $l\sim \beta$ and Szeg\"o theorem gives us a formula
+for the determinant of $L\times L$ matrix
+\begin{equation}
+\exp\left( V_{0} L + \sum_{l=1}^{\infty} l V_{l}V_{-l}\right)
+\end{equation}
+Note the infinity in the sum.
+Aristov \cite{Aristov1998} proposes formally cut off this series by $l=L$ (referring to work \cite{Luttinger1963}) and indeed, it gives a result in the limit of $T=0$
\begin{equation}
-\mathrm{Tr}_{d} \left[e^{i \lambda d^{+} d} e^{i \frac{\pi}{2} (d^{+} a + a^{+} d)}\right] = e^{i\lambda a^{+}a}
+-\frac{\lambda^{2}}{2\pi^{2}}\left(\log (2L\sin p_{F})+\gamma_\text{Euler}\right)
\end{equation}
+Nevertheless, the Fisher-Hartwig formula given in \cite{Deift2011}, Eq.~(1.12) does not imply the dependence on $L$ (notation in paper $n$) for non-singular $f$.
+The cutoff is made automatically for $l\sim\beta$, or in other words, the Eq.~(1.12) does not imply the finite $L$ if $T>0$.
+
+For zero temperature the discontinuity forces us to this more general formula in Eq.~(1.12).
+The particular case that interests us is described in \cite{Abanov2011} in Eq.~(B.9) and afterwards.
+The substitution into Eq.~(1.12) of \cite{Deift2011} gives us Eq.~(B.10) in \cite{Abanov2011}.
+Expansion of Eq.~(B.10) in \cite{Abanov2011} for small $\lambda$ gives us very similar result
+\begin{equation}
+-\frac{\lambda^{2}}{2\pi^{2}}\left(\log (2L\sin p_{F})+\gamma_\text{Euler}+1\right)
+\end{equation}
+This result is also mentioned in \cite{LeHur2012}, right after Eq.~(2.49).
+Taking into account the interaction-dependence obtained from the perturbative approach, we get
+\begin{equation}
+-\frac{\lambda^{2}}{2\pi^{2}}\left(K\left[\log (2L\sin p_{F})+\gamma_\text{Euler}\right]+1\right)
+\end{equation}
+The numerical result given by Andreas speaks in favour of this formula:
+\begin{figure}[h]
+\centering
+\includegraphics[scale=.5]{figKG}
+\caption{Analytics and numerics comparison for $p_{F}=\pi/2$ (half-filling)}
+\label{fig:figKG}
+\end{figure}
\bibliographystyle{amsplain}
\bibliography{../../literature/quantinfo, localcites}
diff --git a/figKG.pdf b/figKG.pdf
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diff --git a/localcites.bib b/localcites.bib
index 9b37844b7ac0a58fce8c57da1fa378ba017452e8..a421923d67fbf1dcd0f6eb12e7d6725ed9863283 100644
--- a/localcites.bib
+++ b/localcites.bib
@@ -1,7 +1,7 @@
%% This BibTeX bibliography file was created using BibDesk.
%% http://bibdesk.sourceforge.net/
-%% Created for Alex Kashuba at 2022-06-03 16:14:16 +0200
+%% Created for Alex Kashuba at 2022-10-17 21:18:58 +0200
%% Saved with string encoding Unicode (UTF-8)
@@ -61,10 +61,10 @@
url = {https://en.wikipedia.org/wiki/Baker–Campbell–Hausdorff_formula}}
@inbook{McCoyWu1973,
- author = {B. M. McCoy and T. T. Wu,},
+ author = {B. M. McCoy and T. T. Wu},
chapter = {X},
date-added = {2022-02-02 15:14:29 +0100},
- date-modified = {2022-06-03 16:12:10 +0200},
+ date-modified = {2022-10-17 21:18:57 +0200},
publisher = {Harvard University Press, Cambridge},
title = {The two-dimensional {I}sing model},
year = {1973}}
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