We investigate dynamics of an inference algorithm termed the belief propagation (BP) when employed in spin glass (SG) models and show that its macroscopic behaviors can be traced by recursive updates of certain auxiliary field distributions whose stationary state reproduces the replica symmetric solution offered by the equilibrium analysis. We further provide a compact expression for the instability condition of the BP's fixed point which turns out to be identical to that of instability for breaking the replica symmetry in equilibrium when the number of couplings per spin is infinite. This correspondence is extended to a SG model of finite connectivity to determine the phase diagram, which is numerically supported.
The Derivation of the Exact Internal Energies for Spin Glass Models by Applying the Gauge Theory to the Fortuin-Kasteleyn Representation
Spin glass models with ferromagnetically biased couplings on the Bethe lattice: analytic solutions and numerical simulations
Multicritical points for the spin glass models on hierarchical lattices
