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.

20 pages, introduction revised, Proposition 2 added

References in corpus (6)

• Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model
• The Parisi formula has a unique minimizer
• A Dynamic Programming Approach to the Parisi Functional
• Variational representations for the Parisi functional and the two-dimensional Guerra-Talagrand bound
• Universal structures in some mean field spin glasses, and an application
• Microcanonical analysis of the Random Energy Model in a random magnetic field

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