On the Perturbation Expansion of the KPZ-Equation

Details On the Perturbation Expansion of the KPZ-Equation On the Perturbation Expansion of the KPZ-Equation

1998-02-06

arxiv.org/abs/cond-mat/9802068v2

J. Stat. Phys. 93 (1998) 143-154

Physics

Condensed Matter

Statistical Mechanics

10 pages, Latex, 2nd revised and enlarged version

Scientific paper

We present a simple argument to show that the beta-function of the d-dimensional KPZ-equation (d>=2) is to all orders in perturbation theory given by beta(g) = (d-2) g - 2/(8 pi)^(d/2) Gamma(2-d/2) g^2 . Neither the dynamical exponent z nor the roughness-exponent zeta have any correction in any order of perturbation theory. This shows that standard perturbation theory cannot attain the strong-coupling regime and in addition breaks down at d=4. We also calculate a class of correlation-functions exactly.

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