Electronic Journal of Probability

A duality principle in spin glasses

Antonio Auffinger and Wei-Kuo Chen

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We prove a duality principle that connects the thermodynamic limits of the free energies of the Hamiltonians and their squared interactions. Under the main assumption that the limiting free energy is concave in the squared temperature parameter, we show that this relation is valid in a large class of disordered systems. In particular, when applied to mean field spin glasses, this duality provides an interpretation of the Parisi formula as an inverted variational principle, establishing a prediction of Guerra [13].

Article information

Electron. J. Probab., Volume 22 (2017), paper no. 61, 17 pp.

Received: 5 February 2017
Accepted: 21 May 2017
First available in Project Euclid: 22 July 2017

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Zentralblatt MATH identifier

Primary: 60F10: Large deviations 82D30: Random media, disordered materials (including liquid crystals and spin glasses)

large deviation Legendre duality Parisi formula spin glass

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Auffinger, Antonio; Chen, Wei-Kuo. A duality principle in spin glasses. Electron. J. Probab. 22 (2017), paper no. 61, 17 pp. doi:10.1214/17-EJP70. https://projecteuclid.org/euclid.ejp/1500689052

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