Influence of thermal fluctuations on the geometry of interfaces of the quenched Ising model

We study the role of the quench temperature T-f in the phase-ordering kinetics of the Ising model with single spin flip in d=2,3. Equilibrium interfaces are flat at T-f=0, whereas at T-f>0 they are curved and rough (above the roughening temperature in d=3). We show, by means of scaling arguments and numerical simulations, that this geometrical difference is important for the phase-ordering kinetics as well. In particular, while the growth exponent z=2 of the size of domains L(t)similar to t(1/z) is unaffected by T-f, other exponents related to the interface geometry take different values at T-f=0 or T-f>0. For T-f>0 a crossover phenomenon is observed from an early stage where interfaces are still flat and the system behaves as at T-f=0, to the asymptotic regime with curved interfaces characteristic of T-f>0. Furthermore, it is shown that the roughening length, although subdominant with respect to L(t), produces appreciable correction to scaling up to very long times in d=2.