The Monte Carlo study of structural disorder and anisotropy influence on nonequilibrium critical behavior of 3d Heisenberg model has performed. Superaging effects and three universality classes were identified for easy-axis anisotropy. Easy-plane anisotropy leads to XY-type behavior, which is insensitive to defects.

Jan 1, 20260 citations

Subtlety in the Critical Behavior of the Two Dimensional XY Model

Jae-Kwon Kim

APSMar 1, 19960 citations

Journal of Magnetism and Magnetic Materials

Non-universal critical behavior in the planar XY-model with fourth order anisotropy

David Paul Landau

Published Feb 1, 1983• 33 citations

Publisher

DOI: 10.1016/0304-8853(83)90821-1

Related papers

Dynamical critical behavior of 3D S=1/2 XY model

M. Howard Lee

AIP conference proceedingsJan 1, 19761 citation

Monte Carlo studies of the two-dimensional XY model with four-fold anisotropy

Truong Thi Bach Yen, Le Thi Thao Vien, Nguyễn Trí Tuấn +8 more

Early theoretical studies of the two-dimensional XY model with four-fold anisotropy (XY h 4 ) predicted that any finite anisotropy should completely suppress Kosterlitz–Thouless (KT) transition of the isotropic system and replace it with a second-order phase transition. This prediction is inconsistent with Monte Carlo (MC) simulations, which suggested KT-like behavior at weak anisotropy. To resolve this discrepancy, we performed large-scale MC simulations to systematically examine the XY h 4 model across a wide range of anisotropic strengths. Our results indicate that while weak anisotropy can mimic KT behavior in small systems, a detailed finite-size scaling analysis of larger systems reveals that the temperature derivative of Binder ratio and the correlation length ratio displays scaling behaviors characteristic of a second-order transition even at the weak h 4 values. The critical exponent ν is non-universal and varies continuously with h 4 from weak to strong anisotropy. These findings confirm that XY h 4 model exhibits a second-order phase transition for weak finite anisotropy, effectively reconciling theoretical predictions with numerical observations.Early theoretical studies of the two-dimensional XY model with four-fold anisotropy (XY h 4 ) predicted that any finite anisotropy should completely suppress Kosterlitz–Thouless (KT) transition of the isotropic system and replace it with a second-order phase transition. This prediction is inconsistent with Monte Carlo (MC) simulations, which suggested KT-like behavior at weak anisotropy. To resolve this discrepancy, we performed large-scale MC simulations to systematically examine the XY h 4 model across a wide range of anisotropic strengths. Our results indicate that while weak anisotropy can mimic KT behavior in small systems, a detailed finite-size scaling analysis of larger systems reveals that the temperature derivative of Binder ratio and the correlation length ratio displays scaling behaviors characteristic of a second-order transition even at the weak h 4 values. The critical exponent ν is non-universal and varies continuously with h 4 from weak to strong anisotropy. These findings confirm that XY h 4 model exhibits a second-order phase transition for weak finite anisotropy, effectively reconciling theoretical predictions with numerical observations.

Nuclear Physics BMay 15, 20260 citations

Critical properties of the two-dimensional XY model

Douglas M. Lublin

Jan 1, 19763 citations

Extended scaling behavior of the spatially anisotropic classical XY model in the crossover from three to two dimensions

P. Butera, M. Pernici

The bivariate high-temperature expansion of the spin-spin correlation function of the three-dimensional classical $XY$ (planar rotator) model, with spatially anisotropic nearest-neighbor couplings, is extended from the tenth through the 21st order. The computation is carried out for the simple cubic lattice, in the absence of magnetic field, in the case in which the coupling strength along the $z$ axis of the lattice is different from those along the $x$ and the $y$ axes. It is then possible to determine accurately the critical temperature as function of the parameter $R$ which characterizes the coupling anisotropy and to check numerically the universality, with respect to $R$ , of the critical exponents of the three-dimensional anisotropic system. The analysis of our data also shows that the main predictions of the generalized scaling theory for the crossover from the three-dimensional to the two-dimensional critical behavior are compatible with the series extrapolations.The bivariate high-temperature expansion of the spin-spin correlation function of the three-dimensional classical $XY$ (planar rotator) model, with spatially anisotropic nearest-neighbor couplings, is extended from the tenth through the 21st order. The computation is carried out for the simple cubic lattice, in the absence of magnetic field, in the case in which the coupling strength along the $z$ axis of the lattice is different from those along the $x$ and the $y$ axes. It is then possible to determine accurately the critical temperature as function of the parameter $R$ which characterizes the coupling anisotropy and to check numerically the universality, with respect to $R$, of the critical exponents of the three-dimensional anisotropic system. The analysis of our data also shows that the main predictions of the generalized scaling theory for the crossover from the three-dimensional to the two-dimensional critical behavior are compatible with the series extrapolations.

arXiv:0909.2202Physical Review BAug 14, 20096 citations

STUDY OF THE INFLUENCE OF ANISOTROPY AND STRUCTURAL DEFECTS ON THE NON‑EQUILIBRIUM CRITICAL BEHAVIOR OF THE HEISENBERG MODEL

V.V. Khitrintseva

Jan 1, 20260 citations

Subtlety in the Critical Behavior of the Two Dimensional XY Model

Jae-Kwon Kim

APSMar 1, 19960 citations

The bivariate high-temperature expansion of the spin-spin correlation function of the three-dimensional classical

XY

(planar rotator) model, with spatially anisotropic nearest-neighbor couplings, is extended from the tenth through the 21st order. The computation is carried out for the simple cubic lattice, in the absence of magnetic field, in the case in which the coupling strength along the

z

axis of the lattice is different from those along the

x

and the

y

axes. It is then possible to determine accurately the critical temperature as function of the parameter

R

which characterizes the coupling anisotropy and to check numerically the universality, with respect to

R

, of the critical exponents of the three-dimensional anisotropic system. The analysis of our data also shows that the main predictions of the generalized scaling theory for the crossover from the three-dimensional to the two-dimensional critical behavior are compatible with the series extrapolations.