Electronic Journal of Probability
- Electron. J. Probab.
- Volume 22 (2017), paper no. 61, 17 pp.
A duality principle in spin glasses
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 .
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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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