Upper critical dimension, dynamic exponent, and scaling functions in the mode-coupling theory for the Kardar-Parisi-Zhang equation |
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Authors: | Colaiori F Moore M A |
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Affiliation: | Department of Physics and Astronomy, University of Manchester, Manchester, M13 9PL, United Kingdom. |
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Abstract: | We study the mode-coupling approximation for the Kardar-Parisi-Zhang 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 dc. We find the exact z = 3/2 value in d = 1, and estimate the values z approximately 1.62, z approximately 1.78 in d = 2, 3. The result dc = 4 and the expansion around dc 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. |
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