The Replica Symmetric Formula for the SK Model Revisited

We provide a simple extension of Bolthausen's Morita type proof of the replica symmetric formula [E. Bolthausen, Stat. Mech. of Classical and Disordered Systems, pp. 63-93 (2018)] for the Sherrington-Kirkpatrick model and prove the replica symmetry for all $(β,h)$ that satisfy $β^2 E \operatorname{sech}^2(β\sqrt{q}Z+h) \leq 1$, where $q = E\tanh^2(β\sqrt{q}Z+h)$. Compared to [E. Bolthausen, Stat. Mech. of Classical and Disordered Systems, pp. 63-93 (2018)], the key of the argument is to apply the conditional second moment method to a suitably reduced partition function.

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