Glassy Solutions of the Kardar-Pasrisi-Zhang Equation
Abstract
It is shown that the mode-coupling equations for the strong-coupling limit of the KPZ equation have a solution for d>4 such that the dynamic exponent z is 2 (with possible logarithmic corrections) and that there is a delta function term in the height correlation function <h(k,w)h^*(k,w)> = (A/k^{d+4-z}) \delta(w/k^z) where the amplitude A vanishes as d -> 4. The delta function term implies that some features of the growing surface h(x,t) will persist to all times, as in a glassy state.
Keywords
Cite
@article{arxiv.cond-mat/9407076,
title = {Glassy Solutions of the Kardar-Pasrisi-Zhang Equation},
author = {M. A. Moore and T. Blum J. P. Doherty and M. Marsili and J-P. Bouchaud and P. Claudin},
journal= {arXiv preprint arXiv:cond-mat/9407076},
year = {2009}
}
Comments
11 pages, Revtex, 1 figure available upon request (same as figure 1 in ref [10]) Important corrections have been made which yield a much simpler picture of what is happening. We still find "glassy" solutions for d>4 where z is 2 (with possible logarithmic corrections). However, we now find no glassy solutions below d=4. A (linear) stability analysis (for d>4) has been included. Also one Author has been added