The Legendre Structure of the Parisi Formula

Antonio Auffinger; Wei Kuo Chen

doi:10.1007/s00220-016-2673-0

The Legendre Structure of the Parisi Formula

Antonio Auffinger, Wei Kuo Chen^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

We show that the Parisi formula of the mixed p-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.

Original language	English (US)
Pages (from-to)	751-770
Number of pages	20
Journal	Communications in Mathematical Physics
Volume	348
Issue number	3
DOIs	https://doi.org/10.1007/s00220-016-2673-0
State	Published - Dec 1 2016

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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title = "The Legendre Structure of the Parisi Formula",

abstract = "We show that the Parisi formula of the mixed p-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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AB - We show that the Parisi formula of the mixed p-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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The Legendre Structure of the Parisi Formula

Abstract

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