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

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