Susceptibility and Correlation Function of the Ising Model on the Cayley Tree

Abstract

The exact expressions are given for the correlation functions and the isothermal susceptibility of the Ising model on the finite Cayley tree under zero external field, and for those quantities in the thermodynamic limit. Matsuda's conclusions, the absence of the spontaneous magnetization and the divergence of the susceptibilities, are reconfirmed. It is shown that local properties around the center of the Cayley tree are given by the Bethe approximation in the thermodynamic limit.