Abstract
A new and simple method of applying the idea of real space renormalization group theory to the analysis of Monte Carlo configurations is proposed and applied to the Glauber kinetic Ising model in two and three dimensions, and to the Kawasaki model in two dimensions. Our method, if correct, utilizes how the system approaches its equilibrium; in contrast to most other Monte Carlo investigations there is no need to wait until equilibrium is established. The renormalization analysis takes only a small fraction of the computer time needed to produce the Monte Carlo configurations, and the results are obtained as the system relaxes atT =T c , the critical temperature. The values obtained for the dynamical critical exponent,z, are 2.12 (d=2) and 2.11 (d=3) for the Glauber model, the 3.90 for the two-dimensional Kawasaki model. These results are in good agreement with those obtained by other methods but with smaller error bars in three dimensions.
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Jan, N., Moseley, L.L. & Stauffer, D. Dynamic Monte Carlo renormalization group. J Stat Phys 33, 1–11 (1983). https://doi.org/10.1007/BF01009743
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DOI: https://doi.org/10.1007/BF01009743