From 007665cb8ac8321371cc97430ece918853718626 Mon Sep 17 00:00:00 2001
From: johannes wasmer <johannes.wasmer@gmail.com>
Date: Tue, 10 Sep 2024 05:02:27 +0200
Subject: [PATCH] update jij-prediction
---
presentation/mainmatter/jij-prediction.tex | 8 +++++++-
1 file changed, 7 insertions(+), 1 deletion(-)
diff --git a/presentation/mainmatter/jij-prediction.tex b/presentation/mainmatter/jij-prediction.tex
index 75063d7..fc8d497 100644
--- a/presentation/mainmatter/jij-prediction.tex
+++ b/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}
--
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