The Aizenman-Sims-Starr scheme and Parisi formula for mixed p-spin spherical models
Wei-Kuo Chen
TL;DR
This paper extends the proof of the Parisi formula for spherical p-spin models to include odd p interactions, using the Aizenman-Sims-Starr scheme and recent ultrametricity results.
Contribution
It generalizes the Parisi formula proof to mixed p-spin spherical models with odd p, building on the Aizenman-Sims-Starr scheme and Panchenko's ultrametricity proof.
Findings
Established the Aizenman-Sims-Starr scheme for mixed p-spin models
Proved the Parisi formula for models including odd p interactions
Connected ultrametricity results to the Parisi formula proof
Abstract
The Parisi formula for the free energy in the spherical models with mixed even p-spin interactions was proven in Michel Talagrand [16]. In this paper we study the general mixed p-spin spherical models including p-spin interactions for odd p. We establish the Aizenman-Sims-Starr scheme and from this together with many well-known results and Dmitry Panchenko's recent proof on the Parisi ultrametricity conjecture [11], we prove the Parisi formula.
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Taxonomy
TopicsTheoretical and Computational Physics · Stochastic processes and statistical mechanics · Geometry and complex manifolds