The replica symmetric formula for the SK model revisited

Source abstract

We provide a simple extension of Bolthausen’s Morita-type proof of the replica symmetric formula [E. Bolthausen, “A Morita type proof of the replica-symmetric formula for SK,” in Statistical Mechanics of Classical and Disordered Systems, Springer Proceedings in Mathematics and Statistics (Springer, Cham., 2018), pp. 63–93; arXiv:1809.07972] for the Sherrington–Kirkpatrick model and prove the replica symmetry for all (β, h) that satisfy β2Esech2(βqZ+h)≤1, where q=E⁡tanh2(βqZ+h). Compared to the work of Bolthausen [“A Morita type proof of the replica-symmetric formula for SK,” in Statistical Mechanics of Classical and Disordered Systems, Springer Proceedings in Mathematics and Statistics (Springer, Cham., 2018), pp. 63–93; arXiv:1809.07972], the key of the argument is to apply the conditional second moment method to a suitably reduced partition function.