Physics – Condensed Matter – Statistical Mechanics
Scientific paper
1999-04-28
Phys.Lett.A278:177-183,2001
Physics
Condensed Matter
Statistical Mechanics
V2 --- 6 pages, LaTeX 209, ReV_TeX 3.2. Title changed, presentation clarified, additional discussion added, references updated
Scientific paper
10.1016/S0375-9601(00)00773-8
A functional integral technique is used to study the ultraviolet or short distance properties of the Kardar-Parisi-Zhang (KPZ) equation with white Gaussian noise. We apply this technique to calculate the one-loop effective potential for the KPZ equation. The effective potential is (at least) one-loop ultraviolet renormalizable in 1, 2, and 3 space dimensions, but non-renormalizable in 4 or higher space dimensions. This potential is intimately related to the probability distribution function (PDF) for the spacetime averaged field. For the restricted class of field configurations considered here, the KPZ equation exhibits dynamical symmetry breaking (DSB) via an analog of the Coleman-Weinberg mechanism in 1 and 2 space dimensions, but not in 3 space dimensions.
Hochberg David
Molina--Paris Carmen
Perez--Mercader Juan
Visser Matt
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