Thermal Depinning of Solitons in the Classical XY Chain in a Field

Abstract

At low enough temperatures solitons (domain walls) are at lattice sites in the one­ dimensional, antiferromagnetic, classical XY model in a field. A crossover behavior due to the depinning of solitons by thermal fluctuations is obtained for a correlation function of the spin component perpendicular to the field. In one-dimensional systems with a discrete set of degenerate ground states, there appear solitons as elementary nonlinear excitations/) solitons in these systems are domain walls which separate two domains associated with distinct ground states. Examples of such systems may be found in some magnetic materials. 2 ),3) The influences of solitons on various physical quantities of these systems have extensively been studied in the literature. 4 ) In particular, it has been shown that the long range behavior of certain correlation functions is strongly affected by solitons. Most of the theories which are intended to calculate the effects of .solitons on statistical properties of those systems are based on continuum models or continuum approximations to lattice models. One of the qualitative differences between a lattice model and a continuum model is that a soliton in the former model is more or less pinned at a lattice site whereas a soliton in the latter is free to slide without extra cost of energy. There have been a few attempts 5 ),6) to investigate the lattice­ discreteness corrections to the continuum approximation, but no evidence showing the effects of soliton pinning has been obtained. The purpose of this pape,r is to study the effects of soliton pinning by examining a soliton-sensitive correlation function in a classical spin model, based on the transfer-matrix integral equation, (2) below. We consider a one-dimensional system of classical planar spins in a field, whose Hamiltonian is given by H =~cos(Bj+l- Bj)-B~cosBj, j