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Physical Review A

Statistical Mechanics of the XY Model. III

Eytan Barouch, Barry M. McCoy

Published Jun 1, 1971• 150 citations
Publisher

Abstract

We continue the considerations of the first paper in this series by studying the time dependence of the spin-correlation functions in response to a step-function change in the external magnetic field. We find that these correlation functions exhibit nonergodic behavior.
DOI
10.1103/physreva.3.2137

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The spin-correlation functions of the one-dimensional XYXYXY model are studied in the presence of a constant magnetic field. We find that the asymptotic behavior of these correlation functions depends strongly on the various parameters of the Hamiltonian.
The Liouville equation for the XY\mathrm{XY}XY model is solved exactly, and the magnetization is computed explicitly. Nonergodic behavior of the magnetization is found for a general class of time-dependent magnetic fields.
Out-of-equilibrium behavior is explored in the one-dimensional anisotropic XY model. Initially preparing the system in the isotropic XX model with a linearly varying magnetic field to create a domain-wall magnetization profile, dynamics is generated by rapidly changing the exchange interaction anisotropy and external magnetic field. Relaxation to a nonequilibrium steady state is studied analytically at the critical transverse Ising point, where correlation functions may be computed in closed form. For arbitrary values of anisotropy and external field, an effective generalized Gibbs' ensemble is shown to accurately describe observables in the long-time limit. Additionally, we find spatial oscillations in the exponentially decaying, transverse spin-spin correlation functions with wavelength set by the magnetization jump across the initial domain wall. This wavelength depends only weakly on anisotropy and magnetic field in contrast to the current, which is highly dependent on these parameters.