Statistical mechanics of one-dimensional complex scalar fields with phase anisotropy

Abstract

The authors investigate the statistical mechanics of a model Lagrangian involving a complex scalar field for which the equations of motion possess solitary-wave solutions due to phase anisotropy. Using a transfer-operator technique, the authors find that the low-temperature correlation length for the field grows exponentially with decreasing temperature, at a rate determined by the activation energy for the solitary wave. This activation energy exhibits a crossover from that for a purely real "${\phi }^4$" scalar kink to that for a phase-only sine-Gordon soliton as the magnitude of the anisotropy potential is decreased past a point where the exact solitary-wave solution is known to "bifurcate." It is concluded that these nonlinear excitations of the complex scalar field are "elementary" in the same sense as real scalar solitary waves are elementary excitations of real one-component fields.