The Cavity Method (Mézard & Parisi, 2001) is the physical basis for Belief Propagation on factor graphs. Remove a variable node i, creating a "cavity." The marginals of the remaining system in this cavity factorize (Bethe approximation = tree-like neighborhood assumption).
Messages η_{i→a} flow from variable i to factor a, and η_{a→i} from factor a to variable i:
η_{i→a}(s_i) ∝ Π_{b≠a} η_{b→i}(s_i)
Iteration converges to marginals on sparse random graphs (locally tree-like). The survey propagation extension handles spin glass phase via distributions over messages.