Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2000-10-26
Physics
Condensed Matter
Statistical Mechanics
RevTex, 4 pages
Scientific paper
10.1103/PhysRevLett.86.3946
We study the mode-coupling approximation for the KPZ equation in the strong coupling 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-(d-4)/4+O((4-d)^2) around d_c. We find the exact z=3/2 value in d=1, and estimate the values 1.62, 1.78 for z, 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.
Colaiori Francesca
Moore Anna M.
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