The Parisi formula for mixed $p$-spin models

Abstract

The Parisi formula for the free energy in the Sherrington-Kirkpatrick and mixed $p$-spin models for even $p\ge 2$ was proved in the seminal work of Michel Talagrand [Ann. of Math. (2) 163 (2006) 221-263]. In this paper we prove the Parisi formula for general mixed $p$-spin models which also include $p$-spin interactions for odd $p$. Most of the ideas used in the paper are well known and can now be combined following a recent proof of the Parisi ultrametricity conjecture in [Ann. of Math. (2) 177 (2013) 383-393].

Published in at http://dx.doi.org/10.1214/12-AOP800 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (1)

• Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model

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