Open Access
May 2014 The Parisi formula for mixed $p$-spin models
Dmitry Panchenko
Ann. Probab. 42(3): 946-958 (May 2014). DOI: 10.1214/12-AOP800


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].


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Dmitry Panchenko. "The Parisi formula for mixed $p$-spin models." Ann. Probab. 42 (3) 946 - 958, May 2014.


Published: May 2014
First available in Project Euclid: 26 March 2014

zbMATH: 1292.82020
MathSciNet: MR3189062
Digital Object Identifier: 10.1214/12-AOP800

Primary: 60K35 , 82B44

Keywords: Free energy , Sherrington–Kirkpatrick model , Ultrametricity

Rights: Copyright © 2014 Institute of Mathematical Statistics

Vol.42 • No. 3 • May 2014
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