Dynamic Monte Carlo renormalization group

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 =Tc, 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.

[1]  P. C. Hohenberg,et al.  Renormalization-group methods for critical dynamics: I. Recursion relations and effects of energy conservation , 1974 .

[2]  K. Binder.  Monte Carlo methods in statistical physics , 1979 .

[3]  Peter Reynolds,et al.  Large-cell Monte Carlo renormalization group for percolation , 1980 .

[4]  Shang‐keng Ma.  Renormalization Group by Monte Carlo Methods , 1976 .

[5]  D. Stauffer.  Coarse graining, Monte Carlo renormalisation, percolation threshold and critical temperature in the Ising model , 1984 .

[6]  J. M. J. van Leeuwen,et al.  Real-Space Renormalization , 1982 .

[7]  D. Stauffer,et al.  Determination of the nonlinear relaxation exponent: A Monte Carlo study , 1982 .

[8]  Robert H. Swendsen,et al.  Monte Carlo Renormalization Group , 1979 .

[9]  Dietrich Stauffer,et al.  Monte Carlo simulation of very large kinetic Ising models , 1981 .

[10]  C. Kalle,et al.  Vectorised dynamics Monte Carlo renormalisation group for the Ising model , 1984 .

[11]  M. Yalabik,et al.  Monte Carlo renormalization-group studies of kinetic Ising models , 1982 .

[12]  H. Janssen,et al.  Critical Dynamics of an Interface in 1+∊ Dimensions , 1981 .

[13]  R. Maynard,et al.  Critical dynamics of finite Ising model , 1982 .

[14]  J. Tobochnik,et al.  Dynamic Monte Carlo Renormalization Group , 1981 .

[15]  Hans J. Herrmann,et al.  Tests of the multi-spin-coding technique in Monte Carlo simulations of statistical systems , 1981 .

[16]  J. Gunton,et al.  Monte Carlo renormalization-group study of the two-dimensional Glauber model , 1982 .