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Modern Physics Letters B

SHORT-TIME CRITICAL DYNAMICS OF MULTISPIN INTERACTION ISING MODEL IN TWO DIMENSIONS

L. WANG, J. B. Zhang, H. P. Ying, Da-Ren Ji

Published Dec 10, 1999• 4 citations
Publisher

Abstract

We investigated the short-time dynamics of a multispin model in two dimensions. A dynamical Monte Carlo simulation which avoids the critical slowing down is performed at critical temperature and the short-time dynamic scaling behavior is found. By using the universal power-law scaling features, the critical exponents θ, z and 2β/ν are estimated in our calculations.

DOI
10.1142/s021798499900124x

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We investigated the short-time dynamics of a multispin model in two dimensions. A dynamical Monte Carlo simulation which avoids the critical slowing down is performed at critical temperature and the short-time dynamic scaling behavior is found. By using the universal power-law scaling features, the critical exponents θ, z and 2β/ν are estimated in our calculations.
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Monte Carlo simulations of critical dynamics has been used to study the short-time process and scaling behavior of two-layer Ising model. The result shows that there are critical points even when the coupling between the two layers is not equal to zero; the short-time dynamic critical exponent θ was determined; the traditional critical exponent 1/νz was estimated also.Our result encouraged the supposition of the existence of the critical line and evidenced that this model was likely a weak universal model.
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.
Monte Carlo simulations of the short-time critical dynamics are reviewed. The short-time universal scaling behavior of the dynamic Ising model and Potts model are discussed in detail, while extension and application to more complex systems as the XY model, the fully frustrated XY model and other dynamic systems are also presented. The investigation of the universal behavior of the short-time dynamics not only enlarges the fundamental knowledge on critical phenomena but also, more interestingly, provides possible new ways to determine not only the new critical exponents θ and θ1, but also the traditional dynamic critical exponent z as well as all static critical exponents.