On the Perturbation Expansion of the KPZ Equation

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We present a simple argument to show that the β-function of the d-dimensional KPZ equation (d ≥ 2) is to all orders in perturbation theory given by β (gR) = (d −2) gR − [2/(8π)d/2] Γ (2 − d/2)g2R Neither the dynamical exponent z nor the roughness exponent ζ 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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