Unusual features of coarsening when detachment rates decrease with cluster mass

Abstract

We study conserved one-dimensional models of particle diffusion, attachment, and detachment from clusters, where the detachment rates decrease with increasing cluster size as gamma(m) approximately m(-k), k>0 . Heuristic scaling arguments based on random walk properties show that the typical cluster size scales as (t/ln t)z , with z=1/(k+2) . The coarsening of neighboring clusters is characterized by initial symmetric flux of particles between them followed by an effectively asymmetric flux due to the unbalanced detachment rates, which leads to the above logarithmic corrections. Small clusters have densities of order t(-mz)(1), with z(1)=k/(k+2) . Thus for k<1 , the small clusters (mass of order unity) are statistically dominant and the average cluster size does not scale as the size of typically large clusters does. We also solve the master equation of the model under an independent interval approximation, which yields cluster distributions and exponent relations and gives the correct dominant coarsening exponent after suitable changes to incorporate effects of correlations. The coarsening of typical large clusters is described by the distribution Pt(m) approximately 1/ty f(m/tz) , with y=2z . All results are confirmed by simulation, which also illustrates the unusual features of cluster size distributions, with a power-law decay for small masses and a negatively skewed peak in the scaling region. The detachment rates considered here can apply in the presence of strong attractive interactions, and recent applications suggest that even more rapid rate decays are also physically realistic.