Statistical Physics and Interdisciplinary Applications

Spin glasses are ubiquitous models because of their statistical physics properties, and also because they are one of the simplest models where inference algorithms can be tested. We study the application of message passing inference algorithms to finite dimensional Edwards Anderson model. While the naive belief propagation (Bethe approximation) is quite poor in finite dimensional lattice, and does not converge at low temperatures, the generalized belief propagation algorithm shall be a more powerful approximation, but also suffer from convergence problems. We develop a (generalized) message passing algorithm for solving the stationary points of the free energy Edwards Anderson model in 2D and 3D. The messages flow from square plaquettes to links in the graph, and are equivalent to a naive Belief Propagation algorithm in a dual lattice. With the drawback that only the ferromagnetic phase can be explored with our algorithm, it reproduces the results obtained by more general algorithms (GBP-DoubleLoop) in a time that is 3 orders of magnitude smaller. We show the results for the energy at different temperatures for the 2D and 3D models, comparing it with the exact (Monte Carlo) results. The correspondence between exact correlations and inferred correlations of neighboring spins is quite good, specially in 2D model. From a correlation information, a decimation
procedure is implemented to find an approximation to the ground state configuration.