Affiliation:
1. Institute for Applied Mathematics, University of Bonn, Endenicher Allee 60, 53115 Bonn, Germany
2. Department of Mathematics, Harvard University, One Oxford Street, Cambridge, Massachusetts 02138, USA
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 [Formula: see text], where [Formula: see text]. 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.
Funder
National Science Foundation
Simons Foundation
Subject
Mathematical Physics,Statistical and Nonlinear Physics
Cited by
2 articles.
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