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arXiv · 2212.14476

The Two Point Function of the SK Model without External Field at High Temperature

Christian Brennecke·Adrien Schertzer·Changji Xu·Horng-Tzer Yau
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Abstract

We show that the two point correlation matrix $ \textbf{M}= (\langle σ_i σ_j\rangle)_{1\leq i,j\leq N} $ of the Sherrington-Kirkpatrick model with zero external field satisfies \[ \lim_{N\to\infty} \| \textbf{M} - ( 1+β^2 - β\textbf{G})^{-1} \|_{\text{op}} =0 \] in probability, in the full high temperature regime $β< 1$. Here, $\textbf{G}$ denotes the GOE interaction matrix of the model.

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Christian Brennecke, Adrien Schertzer, Changji Xu, Horng-Tzer Yau. 2023-11-08. The Two Point Function of the SK Model without External Field at High Temperature. https://doi.org/10.2140/pmp.2024.5.131

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