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Numerical Confirmation of Late-time t^{1/2} Growth in Three-dimensional Phase Ordering

Gregory Brown·Per Arne Rikvold
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Abstract

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 ($700^3$) at late times, $t \ge 150,$ the characteristic length grows as a power law, $R(t) \sim t^n$, with the measured $n$ in agreement with the theoretically expected result $n=1/2$ to within statistical errors. In this time regime $R(t)$ is found to be in excellent agreement with the analytical result of Ohta, Jasnow, and Kawasaki [Phys. Rev. Lett. {\bf 49}, 1223 (1982)]. At early times, good agreement is found between the simulations and the linearized theory with corrections due to the lattice anisotropy.

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Gregory Brown, Per Arne Rikvold. 2001-11-02. Numerical Confirmation of Late-time t^{1/2} Growth in Three-dimensional Phase Ordering. https://doi.org/10.1103/physreve.65.036137

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