NONEQUILIBRIUM DYNAMICS OF THE ISING-MODEL FOR T-LESS-THAN-OR-EQUAL-TO-TC

The growth of order in Ising models with non-conserved order parameter is considered for quenches to final temperatures T(f) = 0 and T(f) = T(c). The results of numerical simulations in spatial dimension d = 2 are presented. In all cases a scaling regime is entered for sufficiently long times, where the characteristic length scale is the 'domain size', L(t) approximately t1/2, for T(f) = 0, and the 'non-equilibrium correlation length', xi(t) approximately t1/z, for T(f) = T(c). The equal-time correlation function has the expected scaling forms f(r/L(t)) and r-(d-2+-eta)f(c)(r/xi(t)) for T(f) = 0 and T(c) respectively. The scaling function f(c)(x) has interesting short-distance behaviour which is elucidated using scaling arguments and by epsilon- and 1/n-expansions. The T = 0 scaling function f(x) depends on whether the spin correlations present in the initial conditions are of long or short range, as does the exponent lambda-BAR which describes the decay of the autocorrelation function, A(t) = [<S(i)(t)>S(i)(0)] approximately L(t) -lambda-BAR. Results for a quench from the equilibrium critical state to T(f) = 0 are consistent with theoretical predictions.