Inference algorithm for finite-dimensional spin glasses: Belief propagation on the dual lattice

摘要: Starting from a cluster variational method, and inspired by the correctness of paramagnetic ansatz [at high temperatures in general, at any temperature two-dimensional (2D) Edwards-Anderson (EA) model] we propose message-passing algorithm--the dual algorithm--to estimate marginal probabilities spin glasses on finite-dimensional lattices. We use EA models 2D 3D as benchmarks. The algorithm improves Bethe approximation, show that wide range (compared to critical temperature) our compares very well with Monte Carlo simulations, double-loop algorithm, exact calculation ground state systems bimodal Gaussian interactions. Moreover, it is usually 100 times faster than other provably convergent methods, algorithm. In quality inference deteriorates only where correlation length becomes large, i.e., low close 3D.