Non-equilibrium dynamics of the Ising model for T less-than/equal-toT_c

Abstract

The growth of order in Ising models with nonconserved order parameter is considered for quenches to final temperatures Tf=0 and Tf=Tc. 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 t12/, for Tf=0, and the 'nonequilibrium correlation length', xi (t) approximately t1z/, for Tf=Tc. The equal-time correlation function has the expected scaling forms f(r/L(t)) and r-(d-2+ eta )fc(r/ xi (t)) for Tf=0 and Tc respectively. The scaling function fc(x) has interesting short-distance behaviour which is elucidated using scaling arguments and by in - 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 which describes the decay of the autocorrelation function, A(t)=((Si(t))Si(O)) approximately L(t)-. Results for a quench from the equilibrium critical state to Tf=0 are consistent with theoretical predictions.