Surface statistics in ASOS, RSOS and BCSOS roughening models

Abstract

The local height distribution is studied by a low temperature expansion for different versions of the SOS picture of a smooth surface; the exact Gaussian solution for the BCSOS model does not hold in the ASOS and RSOS pictures, in particular the ASOS distribution seems to be far from Gaussian behaviour. In the Gaussian limit (BCSOS), the asymptotic value of the characteristic function is evaluated exactly with and without screening effects and a rapidly convergent expansion near T R is obtained, showing that the usual Gaussian approximation holds only at high temperatures and far from destructive interference conditions. The critical behaviour of some fundamental quantities is studied.