Monte Carlo renormalization-group study on the two-dimensional spin-1 Ising model

John P. Bartel

Kenneth Geddes Wilson

Qing-Kuan Meng, Dong-Tai Feng, Yuping Sun +3 more

Sheldon L. Katz, J. D. Gunton, Chao Ping Liu

A recent Monte Carlo renormalization-group study of the two-dimensional kinetic Ising model is extended to obtain renormalized time correlation functions from initial lattices of 16 \ifmmode\times\else\texttimes\fi{} 16 and 32 \ifmmode\times\else\texttimes\fi{} 32 spins. Different ways to estimate the dynamical exponent $z$ are discussed, with our "best" estimate of $z\ensuremath{\simeq}2.23$ being consistent with the original study.

John P. Bartel

The critical dynamics of the two dimensional Kinetic Ising Model have been studied using Monte Carlo Real Space Renormalization Group techniques. Time dependent correlation functions were calculated for square lattices of 16 x 16 and 32 x 32 spins, using periodic boundary conditions wth 60,000 and 15,000 Monte Carlo steps per spin, respectively;The critical exponent z was estimated using a matching process for a variety of renormalization group operators. The estimates for z were surprisingly sensitive to small changes in the value of the renormalization group operator, with physically reasonable operators giving estimates for z less than the rigorous lower bound for z of z(,o) = 1.75. The estimates for z from a given renormalization group operator showed poor convergence properties. Attempts to estimate z from the scaling form of the correlation function were inconclusive, as were attempts to estimate the static exponent (eta);Possible explanations of these unexpected results are discussed. The most plausible source of the complex behavior seen in this work is the discrete nature of time in the Monte Carlo computer simulation, which generates phenomena not present in standard theoretical treatments of the Kinetic Ising Model.

Henk W. J. Blöte, Aaldert Compagner, J. H. Croockewit +5 more