The Annals of Probability

The Parisi formula for mixed $p$-spin models

Dmitry Panchenko

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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].

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Ann. Probab. Volume 42, Number 3 (2014), 946-958.

First available in Project Euclid: 26 March 2014

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Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82B44: Disordered systems (random Ising models, random Schrödinger operators, etc.)

Sherrington–Kirkpatrick model free energy ultrametricity


Panchenko, Dmitry. The Parisi formula for mixed $p$-spin models. Ann. Probab. 42 (2014), no. 3, 946--958. doi:10.1214/12-AOP800.

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