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We prove that the two point correlation matrix $ \textbf{M}= (\langle\sigma_i ; \sigma_j\rangle)_{1\leq i,j\leq N} \in \mathbb{R}^{N\times N}$ ofthe Sherrington-Kirkpatrick model has the property that for every $\epsilon>0$there exists $K_\epsilon>0$, that is independent of $N$, such that  \[ \mathbb{P}\big( \| \textbf{M} \|_{\text{op}} \leq K_{\epsilon}\big) \geq1- \epsilon \] for $N$ large enough, for suitable interaction and externalfield parameters $(\beta,h)$ in the replica symmetric region. In other words,the operator norm of $\textbf{M}$ is of order one with high probability. Ourresults are in particular valid for all $ (\beta,h)\in (0,1)\times (0,\infty) $and thus complement recently obtained results in \cite{EAG,BSXY} that imply theoperator norm boundedness of $\textbf{M}$ for all $\beta<1$ in the special caseof vanishing external field.

Operator Norm Bounds on the Correlation Matrix of the SK Model at High Temperature