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].
CITATION STYLE
Auffinger, A., & Chen, W. K. (2017). A duality principle in spin glasses. Electronic Journal of Probability, 22. https://doi.org/10.1214/17-EJP70
Mendeley helps you to discover research relevant for your work.