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

We show that the two point correlation matrix $\mathbf{\text{M}}=(⟨{\sigma }_i{\sigma }_j⟩{)}_{1\le i,j\le N}$ of the Sherrington-Kirkpatrick model with zero external field satisfies $$\underset{N\to \mathrm{\infty }}{\lim }\mathrm{\parallel }\mathbf{\text{M}}-(1+{\beta }^2-\beta \mathbf{\text{G}}{)}^{-1}{\mathrm{\parallel }}_{\text{op}}=0$$ in probability, in the full high temperature regime $\beta <1$. Here, $\mathbf{\text{G}}$ denotes the GOE interaction matrix of the model.