Finite-size calculations for the kinetic Ising model

Abstract

Using a Hamiltonian formulation of the master equation, we carry out finite-size calculations for the dynamical critical exponent z of the kinetic Ising model in one and two dimensions. In one dimension, different appropriately normalized transition probabilities give different values for z; this result is based on both exact and finite-size calculations. We show that this "nonuniversal" behavior is due to the fact that the critical temperature for the one-dimensional Ising model is zero. In two dimensions we combine our finite-size calculations with finite-size scaling theory to calculate z. Even in this case we find that z depends on the form of the transition probability-a result that contradicts the universality hypothesis for dynamical critical behavior. We discuss the possible reasons for this contradiction.