Exactly Soluble Models of Quantum Systems Showing the Second Order Phase Transitions

Abstract

A theorem is given for calculating the partition function of quantum mechanical systems. Using this theorem, it is shown that some sort of long-range interaction is equivalent to an effective field. The exact solution of linear anisotropic Heisenberg model with staggered fields, and consequently the zero field staggered susceptibility are given. Finally, it is shown that due to the effect of the transverse components, the value of the Curie point decreases both in the ferromagnetic and antiferromagnetic cases. The rate of decreases in the antiferromagnetic case is smaller than in the ferromagnetic case.