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Journal of Applied Physics

Excitations in the classical X Y chain

R. W. Gerling, David Paul Landau, Murty S. S. Challa

Published Nov 15, 1988• 2 citations
Publisher

Abstract

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.

DOI
10.1063/1.342187

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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.
We have investigated the time-dependent behavior of the classical XY chain in a symmetry-breaking anisotropy field using an ultrafast spin-dynamics method in which we integrate the equation of motion with equilibrium spin configurations determined by Monte Carlo simulations. All three polarizations of the scattering function S(q,\ensuremath{\omega}) were determined for temperature kB{\mathit{k}}_{\mathit{B}}kB​T=0.2J and fields varying from 0.1J to 0.6J. Substantial differences are found as compared with the isotropic ferromagnetic chain in a transverse magnetic field. The soliton contribution, single-spin-wave peaks, and both the sum and difference two-spin-wave contributions are separated. Half-widths and integrated intensities are extracted and compared with theoretical predictions based on mapping onto the sine-Gordon model.
The time-dependent behavior of the classical, ferromagnetic xy chain in a symmetry-breaking magnetic field was studied using a very fast, vectorized spin-dynamics method. The equations of motion were integrated using starting configurations determined by Monte Carlo simulations. By calculating spin-spin correlation functions and taking space-time Fourier transforms, we determined S(q,\ensuremath{\omega}) for a wide range of fields and temperatures. We identify and measure the characteristics of single spin-wave peaks and two spin-wave sum peaks, as well as central peaks due to both soliton and two spin-wave difference processes. These results are discussed in light of existing theory and experiments.
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.
The classical one-dimensional XY model in a symmetry-breaking Gaussian-distributed random magnetic field was studied using an ultrafast, vectorized spin-dynamics program on a Cray Y-MP. We calculated the time- and space-displaced spin-spin correlation functions, which was then Fourier-transformed to get the neutron-scattering law S(q,\ensuremath{\omega}). We see a clear change of the different contributions when the random field is switched on. At low temperatures the random field induces significant increases in the soliton density.
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.