Solid-on-solid model for surface growth in 2+1 dimensions

We analyze in detail the solid-on-solid (SOS) model for growth processes on a square substrate in 2+1 dimensions. By using the Markovian surface properties, we introduce an alternative approach for determining the roughness exponent of a special type of SOS model—the restricted-solid-on-solid (RSOS) model—in 2+1 dimensions. This model is the SOS model with the additional restriction that the height difference must be S  =1. Our numerical results show that the behavior of the SOS model in 2+1 dimensions for approximately S≥S×∼8S≥S×∼8 belongs to the two different universality classes: during the initial time stage, t