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Journal of Physics A Mathematical and General

Short-time scaling in the critical dynamics of an antiferromagnetic Ising system with conserved magnetization

Parongama Sen, Subinay Dasgupta

Published Mar 15, 2002• 4 citations
Publisher

Abstract

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 .

DOI
10.1088/0305-4470/35/12/305

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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 .
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​.
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.
In this work the two-dimensional Ising model with nearest- and next-nearest-neighbor interactions is revisited. We obtain the dynamic critical exponents z and θ from short-time Monte Carlo simulations. The dynamic critical exponent z is obtained from the time behavior of the ratio [Formula: see text], whereas the non-universal exponent θ is estimated from the time correlation of the order parameter <M(0)M(t)> ~ tθ, where M(t) is the order parameter at instant t, d is the dimension of the system and <(⋯)> is the average of the quantity (⋯) over different samples. We also obtain the static critical exponents β and ν by investigating the time behavior of the magnetization.