Physics – Condensed Matter
Scientific paper
1997-11-05
Phys. Rev. Lett. 80, 2366 (1998)
Physics
Condensed Matter
4 pages, revtex, no figures
Scientific paper
10.1103/PhysRevLett.80.2366
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.
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