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arXiv:1210.1499 · Progress of Theoretical Physics

Non-Equilibrium Critical Relaxation of the 3D Heisenberg Magnets with Long-Range Correlated Disorder

Pavel Vladimirovich Prudnikov, Maria A. Medvedeva

Published Mar 1, 2012• 16 citations
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Abstract

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. The static and dynamic critical exponents are determined for systems starting from an ordered initial state. The obtained values of the exponents are in good agreement with results of the field-theoretic description of the critical behavior of this model in the two-loop approximation.

DOI
10.1143/ptp.127.369

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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.
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.
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.
Employing Monte Carlo simulations, the equilibrium dynamic critical behavior or L×L×L simple cubic classical Heisenberg models with periodic boundary conditions are determined. From the long-time exponential decay of the time-displaced correlation function of the magnetization the linear (equilibrium) relaxation time τ is also determined. It is found that at the critical point Tc, τ grows like τ≂Lz with z=1.94±0.06. In the paramagnetic region a power-law divergence τ≂(T/Tc−1)−Δ was found with Δ=zν=1.38±0.04, which implies a dynamical critical exponent z=1.96±0.07. Both values are consistent with theoretical predictions and results of experimental studies concerning the dynamical critical behavior of Heisenberg magnets perturbed by order-parameter nonconserving forces.