Velocity Distribution of Topological Defects in Phase-Ordering Systems

Abstract

The distribution of interface (domain-wall) velocities $\mathbf{v}$ in a phase-ordering system is considered. Heuristic scaling arguments based on the disappearance of small domains lead to a power-law tail, $P_v(v)\sim v^{-p}$ for large v, in the distribution of $v\equiv |\mathbf{v}|$. The exponent p is given by $p=2+d/(z-1)$, where d is the space dimension and 1/z is the growth exponent, i.e. z=2 for nonconserved (model A) dynamics and z=3 for the conserved case (model B). The nonconserved result is exemplified by an approximate calculation of the full distribution using a gaussian closure scheme. The heuristic arguments are readily generalized to conserved case (model B). The nonconserved result is exemplified by an approximate calculation of the full distribution using a gaussian closure scheme. The heuristic arguments are readily generalized to systems described by a vector order parameter.

5 pages, Revtex, no figures, minor revisions and updates, to appear in Physical Review E (May 1, 1997)

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