Quantized Scaling of Growing Surfaces

Abstract

The Kardar-Parisi-Zhang universality class of stochastic surface growth is studied by exact field-theoretic methods. From previous numerical results, a few qualitative assumptions are inferred. In particular, height correlations should satisfy an operator product expansion and, unlike the correlations in a turbulent fluid, exhibit no multiscaling. These properties impose a quantization condition on the roughness exponent $\chi$ and the dynamic exponent $z$. Hence the exact values $\chi =2/5,z=8/5$ for two-dimensional and $\chi =2/7,z=12/7$ for three-dimensional surfaces are derived.

4 pages, revtex, no figures

References in corpus (1)

• Critical Discussion of the 2-Loop Calculations for the KPZ-Equation

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