## Electronic Journal of Probability

### A duality principle in spin glasses

#### Abstract

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

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

Dates
Accepted: 21 May 2017
First available in Project Euclid: 22 July 2017

https://projecteuclid.org/euclid.ejp/1500689052

Digital Object Identifier
doi:10.1214/17-EJP70

Mathematical Reviews number (MathSciNet)
MR3683370

Zentralblatt MATH identifier
1379.60028

#### Citation

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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