Bethe Lattice and the Bethe Approximation

Abstract

Statistical mechanics of the Bethe lattice was developed. Properties of the Bethe lattice, i. e., (of the Bethe approximation) were summarized including low temperature susceptibilities of ferro- and antiferromagnets. The equivalence of the exact solution of the Bethe lattice to the Bethe approximation of the Ising model in the case of the antiferromagnetism was shown. The partition function of the Bethe lattice with first and second neighbor interactions was obtained and the critical temperature was calculated in the case where the first neighbor interaction is ferromagnetic.