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arXiv:cond-mat/0103136 · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Monte Carlo simulations of short-time critical dynamics with a conserved quantity

Bo Zheng, H. J. Luo

Published May 25, 2001• 17 citations
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Abstract

With Monte Carlo simulations, we investigate short-time critical dynamics of the three-dimensional antiferromagnetic Ising model with a globally conserved magnetization m(s) (not the order parameter). From the power law behavior of the staggered magnetization (the order parameter), its second moment and the autocorrelation, we determine all static and dynamic critical exponents as well as the critical temperature. The universality class of m(s)=0 is the same as that without a conserved quantity, but the universality class of nonzero m(s) is different.

DOI
10.1103/physreve.63.066130

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With Monte Carlo simulations, we investigate short-time critical dynamics of the three-dimensional antiferromagnetic Ising model with a globally conserved magnetization m(s) (not the order parameter). From the power law behavior of the staggered magnetization (the order parameter), its second moment and the autocorrelation, we determine all static and dynamic critical exponents as well as the critical temperature. The universality class of m(s)=0 is the same as that without a conserved quantity, but the universality class of nonzero m(s) is different.
We study by Monte Carlo simulation the short-time exponent θ in an antiferromagnetic Ising system for which the magnetization is conserved but the sublattice magnetization (which is the order parameter in this case) is not. This system belongs to the dynamic class of model C. We use nearest-neighbour Kawasaki dynamics so that the magnetization is conserved locally . We find that in three dimensions θ is independent of the conserved magnetization. This is in agreement with the available theoretical studies, but in disagreement with previous simulation studies with a global conservation algorithm. However, we agree with both these studies regarding the result θ C ≠θ A . We also find that in two dimensions, θ C = θ A .
Comprehensive Monte Carlo simulations of the short-time dynamic behaviour are reported for the three-dimensional Ising model at criticality. Besides the exponent of the critical initial increase and the dynamic exponent z , the static critical exponents and as well as the critical temperature are determined from the power-law scaling behaviour of observables at the beginning of the time evolution. States of very high temperature as well as of zero temperature are used as initial states for the simulations.
We study by Monte Carlo simulations the short-time exponent θθθ in an antiferromagnetic Ising system for which the magnetisation is conserved but the sublattice magnetisation (which is the order parameter in this case) is not. This system belongs to the dynamic class of model C. We use nearest neighbour Kawasaki dynamics so that the magnetisation is conserved {\em locally}. We find that in three dimensions θθθ is independent of the conserved magnetisation. This is in agreement with the available theoretical studies, but in disagreement with previous simulation studies with global conservation algorithm. However, we agree with both these studies regarding the result θC≠θAθ_C \ne θ_AθC​=θA​. We also find that in two dimensions, θC=θAθ_C = θ_AθC​=θA​.
Critical scaling and universality in the short-time dynamics for antiferromagnetic models on a three-dimensional stacked triangular lattice are investigated using Monte Carlo simulation. We have determined the critical point by searching for the best power law for the order parameter as a function of time and measured the critical exponents. Our results indicate that it is possible to distinguish weak first-order from second-order phase transitions and confirm that XY antiferromagnetic systems undergo a (weak) first-order phase transition accompanied by pseudocritical scaling.
We employed Monte Carlo simulations and short-time dynamic scaling to determine the static and dynamic critical exponents for the generalized two-dimensional Blume-Capel model of spin-3/2. We showed that the critical behavior at the second-order phase-transition line between the paramagnetic and ferromagnetic phases is in the same universality class of the two-dimensional Ising model. However, at the double critical end point, which is present in the phase diagram of the model, the critical exponent beta , associated to the order parameter, is different from that of the Ising model.