Monte Carlo simulation of very large kinetic Ising models

We study the relaxation of Ising models in three and four dimensions aboveTc, using multi-spin coding for lattices up to 3603 and 404. The nonlinear relaxation time diverges as (T−Tc)−1.05±0.04 in three dimensions, where corrections to scaling are taken into account. In four dimensions the effective exponent is about 0.72; logarithmic correction factors make the analysis difficult here. The linear relaxation time for the asymptotic exponential decay is found to be larger, with effective exponents 1.31 (d=2) and 0.97 (d=4). The difference in the linear and nonlinear relaxation exponents is compatible in three dimensions with the orderparameter exponent β, as predicted by Racz.