Applications of the coherent state representation in the theory of magnetism: I. The Heisenberg model

Abstract

By transforming the Heisenberg model Hamiltonian to Bose operators it becomes possible to define a coherent state representation for the spin system. This representation proves to be a useful basis for evaluating the partition function in a manner similar to that used previously for a superfluid. A hard core repulsive interaction is used to include the effects of the spin commutators exactly. The scattering of two spin waves is solved to all orders of perturbation theory in this formalism and used to rederive the low temperature series expansions due to Dyson. The results using the hard core interaction are compared with those using Dyson's dynamical interaction alone. The method is extended to give some results for the case of an anisotropic exchange interaction.