Loop-corrected belief propagation for lattice spin models

Belief propagation (BP) is a message-passing method for solving probabilistic graphical models. It is very successful in treating disordered models (such as spin glasses) on random graphs. On the other hand, finite-dimensional lattice models have an abundant number of short loops, and the BP method is still far from being satisfactory in treating the complicated loop-induced correlations in these systems. Here we propose a loop-corrected BP method to take into account the effect of short loops in lattice spin models. We demonstrate, through an application to the square-lattice Ising model, that loop-corrected BP improves over the naive BP method significantly. We also implement loop-corrected BP at the coarse-grained region graph level to further boost its performance.Comment: 11 pages, minor changes with new references added. Final version as published in EPJ

Superfluidity and Stabilities of a Bose-Einstein condensate with periodically modulated interatomic interaction

We study theoretically the superfluidity and stability of a Bose-Einstein condensate (BEC) whose interatomic scattering length is periodically modulated with optical Feshbach resonance. Our numerical study finds that the properties of this periodic BEC are strongly influenced by the modulation strength. When the modulation strength is small, only the Bloch waves close to the Brillouin zone edge suffer both Landau and dynamical instabilities. When the modulation strength is strong enough, all Bloch waves become dynamically unstable. In other words, the periodic BEC loses its superfluidity completely.Comment: 5 pages, 5 figure