1112.4814 (Federico Ricci-Tersenghi)

On mean-field approximations for estimating correlations and solving the
inverse Ising problem    [PDF]

Federico Ricci-Tersenghi

I consider mean-field approximations for solving two fundamental problems in Ising models, namely estimating 2-point correlations given the couplings (direct problem) and estimating the couplings given the correlations and the magnetizations (inverse problem). I derive analytical expressions for the Bethe approximation, which allow to solve the problems without running the Susceptibility Propagation algorithm. I compare the accuracy of 5 different mean field approximations on several models (diluted ferromagnets and spin glasses) on random graphs and regular lattices. A simple improvement over these approximations is proposed.

View original: http://arxiv.org/abs/1112.4814