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arXiv:0709.0997 · Progress of Theoretical Physics

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

V. V. Prudnikov, Pavel Vladimirovich Prudnikov, B. Zheng, S. V. Dorofeev, V. Y. Kolesnikov

Published Jun 1, 2007• 27 citations
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Abstract

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.

DOI
10.1143/ptp.117.973

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Monte Carlo simulations of the short-time dynamic behavior are reported for three-dimensional Heisenberg model with long-range correlated disorder at criticality, in the case corresponding to linear defects.Former was carried out both from high-temperature and low-temperature initial states.The static and dynamic critical exponents are determined for systems starting from different initial state.The obtained values of the exponents demonstrated a strong influence of long-range correlated quenched defects on the critical behavior of the systems described by the many-component order parameter.
The simultaneous effect of nonequilibrium initial states and correlation between defects of the structure on the evolution of anisotropic disordered systems at the critical point has been analyzed. The field theory description of the nonequilibrium critical behavior of three-dimensional disordered systems with the longrange correlated defects has been given and the dynamical critical exponent of the short-time evolution has been calculated in the two-loop approximation without the use of the ɛ expansion. The values of the dynamical critical exponent obtained by using various methods for summing asymptotic series have been compared with the results of the computer simulation of the nonequilibrium critical behavior of the three-dimensional disordered Ising model in the short-time regime.
The simultaneous effect of non-equilibrium initial states and correlation betweendefects of the structure on the evolution of anisotropic disordered systems at the critical pointwas analyzed. The field theory description of the non-equilibrium critical behavior of three-dimensional disordered systems with the long-range correlated defects was given and the dy-namical critical exponent of the short-time evolution was calculated in the two-loop approxima-tion without the use of the "-expansion. The values of the dynamical critical exponent obtainedby using various methods for summing asymptotic series were compared with the results ofthe computer simulation of the non-equilibrium critical behavior of the three-dimensional dis-ordered Ising model in the short-time regime.