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.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.

arXiv:1602.08027Physical review. EMay 19, 201623 citations

On correlation functions of the XY model

Anatoli G. Izergin, N. A. Kitanin, N. A. Slavnov

Journal of Mathematical SciencesJan 1, 199825 citations

Renormalization of the anisotropic XY model

A. Drzewiński, Frank W. Daerden

Journal of Magnetism and Magnetic MaterialsFeb 1, 19952 citations

Ferromagnetism in theXYmodel with random threefold anisotropy

Ronald Fisch

A Monte Carlo algorithm has been used to study the XY model with random threefold single-site anisotropy on simple cubic lattices, in the strong-anisotropy limit. The model has a pure XY-like ferromagnetic critical point at ${\mathit{T}}_{\mathit{c}}$ /J=2.190\ifmmode\pm\else\textpm\fi{}0.005. The zero-field thermodynamic functions remain close to those of the simple XY model down to T\ensuremath{\approxeq}2.00J. The ground state has an energy per spin of ${\mathit{E}}_{0}$ /J=-2.2305\ifmmode\pm\else\textpm\fi{}0.0010 and a magnetization per spin of ${\mathit{M}}_{0}$ =0.720\ifmmode\pm\else\textpm\fi{}0.003.A Monte Carlo algorithm has been used to study the XY model with random threefold single-site anisotropy on simple cubic lattices, in the strong-anisotropy limit. The model has a pure XY-like ferromagnetic critical point at ${\mathit{T}}_{\mathit{c}}$/J=2.190\ifmmode\pm\else\textpm\fi{}0.005. The zero-field thermodynamic functions remain close to those of the simple XY model down to T\ensuremath{\approxeq}2.00J. The ground state has an energy per spin of ${\mathit{E}}_{0}$/J=-2.2305\ifmmode\pm\else\textpm\fi{}0.0010 and a magnetization per spin of ${\mathit{M}}_{0}$=0.720\ifmmode\pm\else\textpm\fi{}0.003.

Physical review. B, Condensed matterJul 1, 199212 citations

{\mathit{T}}_{\mathit{c}}

/J=2.190\ifmmode\pm\else\textpm\fi{}0.005. The zero-field thermodynamic functions remain close to those of the simple XY model down to T\ensuremath{\approxeq}2.00J. The ground state has an energy per spin of

{\mathit{E}}_{0}

/J=-2.2305\ifmmode\pm\else\textpm\fi{}0.0010 and a magnetization per spin of

{\mathit{M}}_{0}

=0.720\ifmmode\pm\else\textpm\fi{}0.003.