Upper Critical Dimension, Dynamic Exponent, and Scaling Functions in the ModeCoupling Theory for the KardarParisiZhang Equation
Abstract
We study the modecoupling approximation for the KardarParisiZhang equation in the strongcoupling regime. By constructing an ansatz consistent with the asymptotic forms of the correlation and response functions we determine the upper critical dimension d_{c} = 4 and the expansion z = 2\(d4\)/4+O\(\(4d\)^{2}\) around d_{c}. We find the exact z = 3/2 value in d = 1, and estimate the values z~=1.62, z~=1.78 in d = 2, 3. The result d_{c} = 4 and the expansion around d_{c} are very robust and can be derived just from a mild assumption on the relative scale on which the response and correlation functions vary as z approaches 2.
 Publication:

Physical Review Letters
 Pub Date:
 April 2001
 DOI:
 10.1103/PhysRevLett.86.3946
 arXiv:
 arXiv:condmat/0010410
 Bibcode:
 2001PhRvL..86.3946C
 Keywords:

 Condensed Matter  Statistical Mechanics
 EPrint:
 RevTex, 4 pages