Quantized Scaling of Growing Surfaces

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 {χ} and the dynamic exponent z. Hence the exact values χ0ex0ex=0ex0ex2/5,z0ex0ex=0ex0ex8/5 for two-dimensional and χ0ex0ex=0ex0ex2/7,z0ex0ex=0ex0ex12/7 for three-dimensional surfaces are derived.