Monte Carlo study of growth in the two-dimensional spin-exchange kinetic Ising model

Abstract

Results obtained from extensive Monte Carlo simulations of domain growth in the two-dimensional spin-exchange kinetic Ising model with equal numbers of up and down spins are presented. Using different measures of domain size—including the pair-correlation function, the energy, and circularly-averaged structure factor—the domain size is determined (at T=0.5$T_c$) as a function of time for times up to ${10}^6$ Monte Carlo steps. The growth law R(t)=A+${\mathrm{Bt}}^{1/3}$ is found to provide an excellent fit (within 0.3%) to the data, thus indicating that at long times the classical value of (1/3 for the exponent is correct. It is pointed out that this growth law is equivalent to an effective exponent for all times (as given by Huse) $n_{\mathrm{eff}}$(t)=(1/3-1)/3 C/R(t). No evidence for logarithmic behavior is seen. The self-averaging properties of the various measures of domain size and the variation of the constants A and B with temperature are also discussed. In addition, the scaling of the structure factor and anisotropy effects due to the lattice are examined.