Stretched-exponential behavior in Ising critical dynamics

Abstract

By use of Monte Carlo simulations in 1000² and 100³ Ising systems in the para phase, magnetic relaxation is shown to have a Kohlrausch-type stretched-exponentialbehavior, ℳ(t)~exp(-t/ t)^α, 0<α<1, for t<t_c and normal Debye relaxation with α=1 for t>t_c; the crossover time t_c diverges near the transition point T_c. The average relaxation time t shows normal critical slowing down: t~(T-T_c)^-νz, νzℑ1.8 and 1.1 in dimensions d=2 and 3, respectively. We find α≃0.33 for d=2 and 0.4 for d=3. These are compared with previous observations of stretched-exponential relaxation and critical slowing-down behavior of Ising critical dynamics.