Abstract
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 \(\beta (g_R ) = (d - 2)g_R - [2/(8\pi )^{d/2} ]{\text{ }}\Gamma (2 - d/2)g_R^2 \) 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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Wiese, K.J. On the Perturbation Expansion of the KPZ Equation. Journal of Statistical Physics 93, 143–154 (1998). https://doi.org/10.1023/B:JOSS.0000026730.76868.c4
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DOI: https://doi.org/10.1023/B:JOSS.0000026730.76868.c4