Message-passing Algorithms for the Bidimensional Ising Ferromagnet

Abstract

Message-passing algorithms are exploited to find approximated solutions for discrete spin systems. Many thermodynamic quantities can be obtained, often accurately, by this method. The Ising bidimensional ferromagnet (FIB) is a good trial system used here to test different approximations. We compare algorithmic results with analytic calculations to illustrate the matching between the algorithms named Generalized Belief Propagation (GBP) and a family of free energy variational approximations called Cluster Variation Method (CVM).