Ising model in a transverse field. I. Basic theory

Abstract

A brief review is first made of systems for which the spin-1/2 Ising model in a transverse field provides a useful description (insulating magnetic systems, order-disorder ferroelectrics, cooperative Jahn-Teller systems and other systems with 'pseudo-spin'- phonon interactions). A perturbation expansion is then developed which provides for all temperatures an approximate description of the model. The perturbation series is classified with respect to the small parameter 1/z, where z is the number of psins interacting with a given spin; this generates the molecular-field approximation and the random-phase approximation as the lowest-order description of the thermodynamic functions and correlation functions respectively. The leading-order approximations for the correlation functions, susceptibilities and spectral functions are discussed in detail. The formalism, which is the first application of such techniques to systems with varying magnetization direction, provides a basis for subsequent higher-order calculations of the free energy and correlation functions.