Green's Function Theory of the Two-Dimensional Ising Model –Derivation of the Logarithmic Divergence of the Specific Heat–

Abstract

The S =1/2 Ising model for a square lattice is studied by means of the two-time Green's function method. A simple assumption is introduced associating with the rigorous relations among several spin correlation functions which are derived by this method and any approximations such as decoupling ones for the higher order Green's functions are not used. The specific heat obtained by using this assumption shows the logarithmic divergence just below and just above T c . It is ascertained that the theory issues only the error of order 1/ T 4 in the sum rule and in the susceptibility in the high temperature region.