Gaugeless cluster variational method and message passing. Applications to disordered systems.
by
Alejandro Lage Castellanos(University of Havana)
→
Europe/Stockholm
Description
(Motivation) The connections between Bethe approximation in spin glasses and Belief Propagation algorithms in computer science is now well stablished, including the connections with cavity and replica methods. However Generalizations of replica method to Generalized Belief Propagation is less well understood. An initial approach by T. Rizzo et al, showed how it was formally possible, but since then applications have been limited by nasty numerical difficulties.
(Our work) We show how a different generalization of the message passing from the usual Parent to Child approach, leads to simpler average case equations and therefore opens new opportunities for applications. Furthermore, this approach seems more natural, since it naturally lacks of the gauge invariance in the fields that appears in Parent to Child apporach. We will show how to obtain analytical predictions for the critical temperature in the plaquette-CVM approximation for Ising models in general dimensions, and numerical estimates for Edwards-Anderson model
