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

Abstract

We show that the two point correlation matrix $\text{M}=(⟨{\sigma }_i{\sigma }_j⟩{)}_{1\le i,j\le N}$ 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 $\beta <1$. Here, $\text{G}$ denotes the GOE interaction matrix of the model.

47 pages; substantially revised version accepted for publication in Prob. Math. Phys