Message passing and Monte Carlo algorithms: Connecting fixed points with metastable states

¹ Department of Theoretical Physics, Physics Faculty, University of Havana - La Habana, CP 10400, Cuba
² Dipartimento di Fisica, INFN - Sezione di Roma 1 and CNR - IPCF, UOS di Roma, Università La Sapienza P.le A. Moro 5, 00185 Roma, Italy

Received: 24 June 2014
Accepted: 21 August 2014

Abstract

Mean field-like approximations (including naive mean-field, Bethe and Kikuchi and more general cluster variational methods) are known to stabilize ordered phases at temperatures higher than the thermodynamical transition. For example, in the Edwards-Anderson model in 2 dimensions these approximations predict a spin glass transition at finite T. Here we show that the spin glass solutions of the Cluster Variational Method (CVM) at plaquette level do describe well the actual metastable states of the system. Moreover, we prove that these states can be used to predict non-trivial statistical quantities, like the distribution of the overlap between two replicas. Our results support the idea that message passing algorithms can be helpful to accelerate Monte Carlo simulations in finite-dimensional systems.