H B Heo

Partition functions and metropolis-type evolution rules for surface growth models with constraints.

We study dynamical scaling properties of the surface growth model with the Metropolis-type evolution rule from a partition function Z= sum ([h(r)])II (h(max))(h=h(min))1/2(1+z(n(h))), where z is a fugacity-like quantity and n(h) is the number of sites with height h in a surface configuration [h(r)]. The partition function describes a 2-particle correlated growth model when z=-1 and a self-flattening growth model when z=0. For one-dimensional equilibrium surfaces, the scaling properties for z>or=-1 except z=1 are all one phase with roughness exponent alpha=1/3 and growth exponent beta approximately equal 0.22. For the growing (eroding) surfaces, there exists a phase transition at z=0 from the grooved phase (alpha=1) for -1 0.