ANALYTIC OBSERVATIONS FOR THE D = 1 + 1 BRIDGE SITE (OR SINGLE-STEP) DEPOSITION MODEL

Some exact results for a reversible version of the d = 1 + 1 bridge site (or single-step) deposition model are presented. Exact steady-state properties are determined directly for finite systems with various mean slopes. These show explicitly how the asymptotic growth velocity and fluctuations are quenched as the slope approaches its maximum allowed value. Next, exact hierarchial equations for the dynamics are presented. For the special case of "equilibrium growth," these are analyzed exactly at the pair-correlation level directly for an infinite system. This provided further insight into asymptotic scaling behavior. Finally, the above hierarchy is compared with one generated from a discrete form of the Kardar-Parisi-Zhang equations. Some differences are described.