The Parisi formula for mixed $p$-spin models

By Dmitry Panchenko. 2011

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The Parisi formula for the free energy in the Sherrington-Kirkpatrick and mixed $p$-spin models for even $p\geq2$ 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].

Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/91ef4d6d6254f5adebe76c79ca21e6f31352fd44