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Physica Scripta

The Classical XY-Chain with an In-Plane Magnetic Field

Thomas Delica, Rainer W Gerling, Hajo Leschke

Published Jan 1, 1987• 6 citations
Publisher

Abstract

Thermal properties of the one-dimensional classical XY-model in a symmetry-breaking field are studied by using the transfer-kernel method. The results complete earlier data from Monte-Carlo simulations.
DOI
10.1088/0031-8949/35/1/014

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Results are presented for the static and dynamic behavior of a classical XY-chain in a magnetic field. Equilibrium configurations were produced by an importance sampling Monte Carlo method. Static properties are evaluated from these data and a spin-dynamics method is then used to evaluate time displaced correlation functions. The energy-energy correlation function shows a t−1 behavior for times t≳J−1. The correlation function <Sxi(0)Sxi+r(t)≳ decays to the square of the magnetization for large times, and the correlation function <Syi(0)Sy1+r(t)≳ shows oscillatory behavior.
We have studied the time-dependent behavior of the classical XY chain in a symmetry breaking magnetic field using an ultrafast spin-dynamics method in which we integrate the equations of motion using starting configurations determined by Monte Carlo simulations. We calculated the three polarizations of S(q,ω) separately for temperatures from 0.1 to 1.0 J/kB and fields up to 1.5 J. The soliton contribution, the single-magnon peaks, and both the sum and difference two-magnon contributions are separated; we discuss them in detail and compare them with theoretical predictions.
An important sampling Monte Carlo method is used to study the classical, antiferromagnetic, XY chain in a symmetry breaking uniform magnetic field. From equilibrium configurations we extract values for the bulk properties as well as explicit pictures showing individual spin directions. An analysis of the angles which the spin makes with the field shows clearly the presence of both ‘‘π-like’’ and ‘‘2π-like’’ solitons. We also see two distinct types of ‘‘π-like’’ solitons which differ in their behavior as a function of field. The bulk properties are discussed in terms of both spin waves and soliton excitations.