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The Parisi formula for mixed \(p\)-spin models. (English) Zbl 1292.82020

Summary: The Parisi formula for the free energy in the Sherrington-Kirkpatrick and mixed \(p\)-spin models for even \(p \geq 2\) was proved in the seminal work of M. Talagrand [Ann. Math. (2) 163, No. 1, 221–263 (2006; Zbl 1137.82010)]. 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 [the author, Ann. Math. (2) 177, No. 1, 383–393 (2013; Zbl 1270.60060)].

MSC:

82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics
60K35 Interacting random processes; statistical mechanics type models; percolation theory
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References:

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