Monte Carlo simulations of the short-time dynamic behaviour are reported for three-dimensional Ising model and XY-model with long-range spatially correlated disorder at criticality, in the case corresponding to linear defects. The static and dynamic critical exponents are computed with the use of the corrections to scaling. The obtained values of the exponents are in a good agreement with results of the field-theoretic description of the critical behaviour of this model in the two-loop approximation and with our results of Monte Carlo simulations of three-dimensional Ising model in equilibrium state.Monte Carlo simulations of the short-time dynamic behaviour are reported for three-dimensional Ising model and XY-model with long-range spatially correlated disorder at criticality, in the case corresponding to linear defects. The static and dynamic critical exponents are computed with the use of the corrections to scaling. The obtained values of the exponents are in a good agreement with results of the field-theoretic description of the critical behaviour of this model in the two-loop approximation and with our results of Monte Carlo simulations of three-dimensional Ising model in equilibrium state.

Condensed Matter PhysicsJan 1, 200512 citations

Short-Time Critical Dynamics of the Three-Dimensional Systems with Long-Range Correlated Disorder

V. V. Prudnikov, Pavel Vladimirovich Prudnikov, B. Zheng +2 more

Monte Carlo simulations of the short-time dynamic behavior are reported for three-dimensional Ising and XY models with long-range correlated disorder at criticality, in the case corresponding to linear defects. The static and dynamic critical exponents are determined for systems starting separately from ordered and disordered initial states. The obtained values of the exponents are in good agreement with results of the field-theoretic description of the critical behavior of these models in the two-loop approximation and with our results of Monte Carlo simulations of three-dimensional Ising model in equilibrium state.Monte Carlo simulations of the short-time dynamic behavior are reported for three-dimensional Ising and XY models with long-range correlated disorder at criticality, in the case corresponding to linear defects. The static and dynamic critical exponents are determined for systems starting separately from ordered and disordered initial states. The obtained values of the exponents are in good agreement with results of the field-theoretic description of the critical behavior of these models in the two-loop approximation and with our results of Monte Carlo simulations of three-dimensional Ising model in equilibrium state.

arXiv:0709.0997Progress of Theoretical PhysicsJun 1, 200727 citations

The dynamic critical exponent of the three-dimensional Ising model

R. Matz, D. L. Hunter, Naeem Jan

Journal of Statistical PhysicsFeb 1, 199434 citations

Nonequilibrium relaxation of the two-dimensional Ising model: Series-expansion and Monte Carlo studies

Jian‐Sheng Wang, Chee Kwan Gan

We study the critical relaxation of the two-dimensional Ising model from a fully ordered configuration by series expansion in time $t$ and by Monte Carlo simulation. Both the magnetization $(m)$ and energy series are obtained up to 12th order. An accurate estimate from series analysis for the dynamical critical exponent $z$ is difficult but compatible with 2.2. We also use Monte Carlo simulation to determine an effective exponent, ${z}_{\mathrm{eff}}(t)=\ensuremath{-}\frac{1}{8}d\mathrm{ln}t/d\mathrm{ln}m$, directly from a ratio of three-spin correlation to $m$ . Extrapolation to $\stackrel{\ensuremath{\rightarrow}}{t}\ensuremath{\infty}$ leads to an estimate $z=2.169\ifmmode\pm\else\textpm\fi{}0.003$.We study the critical relaxation of the two-dimensional Ising model from a fully ordered configuration by series expansion in time $t$ and by Monte Carlo simulation. Both the magnetization $(m)$ and energy series are obtained up to 12th order. An accurate estimate from series analysis for the dynamical critical exponent $z$ is difficult but compatible with 2.2. We also use Monte Carlo simulation to determine an effective exponent, ${z}_{\mathrm{eff}}(t)=\ensuremath{-}\frac{1}{8}d\mathrm{ln}t/d\mathrm{ln}m$, directly from a ratio of three-spin correlation to $m$. Extrapolation to $\stackrel{\ensuremath{\rightarrow}}{t}\ensuremath{\infty}$ leads to an estimate $z=2.169\ifmmode\pm\else\textpm\fi{}0.003$.

arXiv:cond-mat/9712198Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsJun 1, 199820 citations

Non-equilibrium critical relaxation of the three-dimensional Ising model

Nobuyasu Ito

Physica A Statistical Mechanics and its ApplicationsFeb 1, 1993107 citations

We study the critical relaxation of the two-dimensional Ising model from a fully ordered configuration by series expansion in time

t

and by Monte Carlo simulation. Both the magnetization

(m)

and energy series are obtained up to 12th order. An accurate estimate from series analysis for the dynamical critical exponent

z

is difficult but compatible with 2.2. We also use Monte Carlo simulation to determine an effective exponent, ${z}_{\mathrm{eff}}(t)=\ensuremath{-}\frac{1}{8}d\mathrm{ln}t/d\mathrm{ln}m$, directly from a ratio of three-spin correlation to

m

. Extrapolation to $\stackrel{\ensuremath{\rightarrow}}{t}\ensuremath{\infty}$ leads to an estimate $z=2.169\ifmmode\pm\else\textpm\fi{}0.003$.