Velocity Distribution of Topological Defects in Phase-Ordering Systems

Details Velocity Distribution of Topological Defects in Phase-Ordering Systems Velocity Distribution of Topological Defects in Phase-Ordering Systems

1996-11-26

arxiv.org/abs/cond-mat/9611209v2

Phys. Rev. E 55, 5297 (1997)

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1103/PhysRevE.55.5297

The distribution of interface (domain-wall) velocities ${\bf v}$ 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 $v \equiv |{\bf v}|$. 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.

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