A duality principle in spin glasses

Citation data:

Electronic Journal of Probability, ISSN: 1083-6489, Vol: 22, Issue: 0

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Antonio Auffinger; Wei-Kuo Chen
Institute of Mathematical Statistics
Mathematics; Decision Sciences
article description
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].