The Legendre structure of the Parisi formula
Antonio Auffinger, Wei-Kuo Chen
TL;DR
This paper reveals the Legendre structure of the Parisi formula in mixed p-spin models, showing its concavity and deriving a new conjugate expression involving inverse temperature and the Parisi measure.
Contribution
It introduces a novel Legendre conjugate formulation of the Parisi formula, highlighting its concavity with respect to squared inverse temperature.
Findings
Parisi formula is concave in squared inverse temperature
New Legendre conjugate expression derived for the Parisi formula
Provides deeper understanding of the thermodynamic structure of spin glasses
Abstract
We show that the Parisi formula of the mixed -spin model is a concave function of the squared inverse temperature. This allows us to derive a new expression for the Parisi formula that involves the inverse temperature and the Parisi measure as Legendre conjugate variables.
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