The cavity method (Mézard-Montanari) / belief propagation gives exact results on the Bethe lattice (infinite regular tree, connectivity z). Each node sends a "cavity field" message to neighbors: h_{i→j} = (1/β)arctanh[tanh(βJ)tanh(βh_{k→i})]. At high T: paramagnetic (m=0); below T_c=J/arctanh(1/√(z-1)): ferromagnetic order. For frustrated/random J: spin glass phase — the replica trick counts disorder-averaged log Z = lim_{n→0}(Z^n−1)/n.