Numerical confirmation of late-time $t^{1/2}$ growth in three-dimensional phase ordering

Results for the late-time regime of phase ordering in three dimensions are reported, based on numerical integration of the time-dependent Ginzburg-Landau equation with nonconserved order parameter at zero temperature. For very large systems ${(700\mathrm{}}^3)$ at late times, $t>~150,$ the characteristic length grows as a power law, $R\left(t\right)\mathrm{}\sim t^n,$ with the measured n in agreement with the theoretically expected result $n=1/2\mathrm{}$ to within statistical errors. In this time regime $R\left(t\right)\mathrm{}$ is found to be in excellent agreement with the analytical result of Ohta, Jasnow, and Kawasaki [Phys. Rev. Lett. 49, 1223 (1982)]. At early times, good agreement is found between the simulations and the linearized theory with corrections due to the lattice anisotropy.