Open Access
2017 A duality principle in spin glasses
Antonio Auffinger, Wei-Kuo Chen
Electron. J. Probab. 22: 1-17 (2017). DOI: 10.1214/17-EJP70


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].


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Antonio Auffinger. Wei-Kuo Chen. "A duality principle in spin glasses." Electron. J. Probab. 22 1 - 17, 2017.


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

zbMATH: 1379.60028
MathSciNet: MR3683370
Digital Object Identifier: 10.1214/17-EJP70

Primary: 60F10 , 82D30

Keywords: large deviation , Legendre duality , Parisi formula , Spin glass

Vol.22 • 2017
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