A spin glass with finite range interactions: More diseases

Abstract
We set up and solve the Bethe approximation for a spin glass with finite range interactions. We obtain the finite z analogue of the Thouless Anderson Palmer equations and the free energy functional at all T. In the configuration averaged theory, the entropy S(T) and all other properties are well behaved on a Cayley tree. For real lattices S(0) = 0, but the specific heat is negative near T = 0 for all but small values of z.