QUANTIZED SCALING OF GROWING SURFACES

The Kardar-Parisi-Zhang universality class of stochastic surface growt h is studied by exact field-theoretic methods. From previous numerical results, a few qualitative assumptions are inferred. In particular, h eight correlations should satisfy an operator product expansion and, u nlike the correlations in a turbulent fluid, exhibit no multiscaling. These properties impose a quantization condition on the roughness expo nent 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-dimension al surfaces are derived.