Antiphase domain growth: Correlation functions and structure factors in the scaling regime

We study the coarsening of three-dimensional antiphase domain structures via Monte Carlo simulations. Linear lattice dimensions of $N=1024$ enable us to reach a scaling regime covering about 2.5 orders of magnitude of linear scale. With short-range interactions on cubic lattices at temperatures of $0.75\phantom{\rule{0.16em}{0ex}}{T}_{\text{c}}$, the resulting antiphase domain structures are isotropic, which allows us to describe the real-space correlation functions by a common function scaled by a time-dependent parameter. We compare abstract Potts models and realistic models of atomic order in compounds and show that those with same ground-state degeneracy $q$ lead to equivalent antiphase domain structures, while the scaling functions for different $q$ show slight but significant deviations. Finally, we quantitatively discuss notions of real-space scale (specific interface area) and reciprocal-space scale (superstructure peak width) and thus give numerically exact values for the corresponding parameter $K$ of the Scherrer equation.