ON ERGODIC RELAXATION TIME IN THE THREE-DIMENSIONAL ISING MODEL

We have studied the dynamical decay of the autocorrelation function of the 3D Ising model for different sizes L = 20-52 of spin cluster-cubes.The behaviour of the longest, ergodic relaxation time, tau(e), of a finite domain below the phase transition temperature T-c was mostly considered for two types of phase transition dynamics. A study of the scaling properties of tau(e) demonstrates a negligible difference between the types of dynamics used, but a considerable difference for different boundary conditions. In contrast to the known result for periodic boundary conditions (tau(e) similar to L-z exp [const(L epsilon(v))(2)], where z and v are the dynamical and correlation length exponents, respectively, and epsilon = 1 similar to T/T-c), the ergodic relaxation time for open boundary conditions is proportional to L-z exp Iconst(L epsilon(v))(2k)] with coeffcient k for lattices explored in this work slightly decreasing with L in between 1.65 and 1.58. This result implies that only the lattices of sizes close to or exceeding L = 300 with open boundary conditions might have ergodic relaxation times similar to those with perodic boundary conditions.