Analytic statistical mechanics for a two-component-kink system

Abstract

We employ the transfer-integral technique to study the classical statistical mechanics of a two-component field governed by the Montonen-Sarker-Trullinger-Bishop (MSTB) Hamiltonian. The two-dimensional pseudo-Schrödinger equation approximation to the transfer-integral eigenvalue problem is separated into two one-dimensional Schrödinger equations by transforming to a coordinate system in which the two-component kink trajectories are constant-coordinate lines. This separation of variables allows us to obtain analytic expressions for the low-temperature free energy and static correlation length and we identify contributions to these quantities from the known topological kink excitations in the MSTB model. In addition, we find an unexpected activated contribution to the free energy which we interpret as due to an unknown nontopological kink excitation whose energy vanishes at the bifurcation point.