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.