update jij-prediction

presentation/mainmatter/jij-prediction.tex

@@ -23,12 +23,18 @@
         Benchmark study of atomistic ML interatomic potentials trained on the exchange
         interaction \(J_{ij}\) for spin dynamics, ongoing
 
+        \[
+          \mathcal{J}_{ij} = -\frac{1}{\pi} \operatorname{Im}
+          \int_{-\infty}^{E_F} \mathrm{d} E \operatorname{Tr}[\delta t_i G_{ij}
+          \delta t_j G_{ji}] \longrightarrow
+        \]
+
         \[
           H = -\frac{1}{2}\sum_{i,j}J_{ij} \, \vec{S}_i \cdot \vec{S}_j \longrightarrow J_{ij} = \sum_k \left( J_{ij}
           \right)_k
         \]
       }
-      \vspace*{0em}
+      \vspace*{-1em}
 
       \begin{columns}
         \begin{column}{0.55\linewidth}