The two point function of the SK model without external field at high temperature

We show that the two point correlation matrix $M = {(⟨ σ_{i} σ_{j} ⟩)}_{1 \leq i, j \leq N}$ of the Sherrington–Kirkpatrick model with zero external field satisfies

\lim_{N \to \infty} ∥ M - {(1 + β^{2} - β G)}^{- 1} ∥_{op} = 0

in probability, in the full high temperature regime $β < 1$ . Here, $G$ denotes the GOE interaction matrix of the model.

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Keywords

mean field spin glasses, random matrices, Sherrington–Kirkpatrick model

Mathematical Subject Classification

Primary: 60K35, 82B44, 82D30

Milestones

Received: 26 January 2023

Revised: 3 October 2023

Accepted: 21 October 2023

Published: 30 January 2024

Authors

Christian Brennecke
Institute for Applied Mathematics University of Bonn Bonn Germany

Adrien Schertzer
Institute for Applied Mathematics University of Bonn Bonn Germany

Changji Xu
Center of Mathematical Sciences and Applications Harvard University Cambridge, MA United States

Horng-Tzer Yau
Department of Mathematics Harvard University Cambridge, MA United States

Vol. 5, No. 1, 2024

Christian Brennecke, Adrien Schertzer, Changji Xu and Horng-Tzer Yau

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors