Fluctuations and lack of self-averaging in the kinetics of domain growth

The fluctuations occurring when an initially disordered system is quenched at timet=0 to a state, where in equilibrium it is ordered, are studied with a scaling theory. Both the mean-sizel(t) d of thed-dimensional ordered domains and their fluctuations in size are found to increase with the same power of the time; their relative size fluctuations are independent of the total volumeL d of the system. This lack of self-averaging is tested for both the Ising model and the φ4 model on the square lattice. Both models exhibit the same lawl(t)=(Rt) x withx=1/2, although the φ4 model has “soft walls”. However, spurious results withx≷1/2 are obtained if “bad” pseudorandom numbers are used, and if the numbern of independent runs is too small (n itself should be of the order of 103). We also predict a critical singularity of the rateR∝(1−T/T c)v(z−1/x),v being the correlation length exponent,z the dynamic exponent. Also quenches to the critical temperatureT c itself are considered, and a related lack of self-averaging in equilibrium computer simulations is pointed out for quantities sampled from thermodynamic fluctuation relations.