We introduce correlated growth into a restricted solid on solid model (RSOS), a stochastic deposition model with a constraint on neighboring height differences. A two-dimensional lattice model is used in which particles are deposited via horizontal Levy flight steps with a step length distribution exponentf. Though RSOS is in the same universality class as ballistic deposition for uncorrelated deposition, it appears to depart from it for strong correlations. Forf=1, the short-range limit is reached and both exponentsβ andχ, which describe the dependence of surface width on time and strip length, tend to 1. Forf>1 we retreat to an enhanced algorithm, searching for growth sites which become excessively rare. We find an unusual short-time dependence, butχ still tends to 1. The number of growth sitesG shows saturation forf<1, while forf⩾1 we observeG/L→0 as the strip lengthL increases. Finally, we test directly the relationship of noise-noise correlation strength tof, and find that a direct comparison between correlated growth models and theoretical predictions for growth with correlated noise is so far unjustified.
[1]
Jin Min Kim,et al.
Growth in a restricted solid-on-solid model.
,
1989
.
[2]
H. Eugene Stanley,et al.
Correlations and Connectivity
,
1990
.
[3]
Zhang,et al.
Burgers equation with correlated noise: Renormalization-group analysis and applications to directed polymers and interface growth.
,
1989,
Physical review. A, General physics.
[4]
Spatially Correlated Ballistic Deposition
,
1989
.
[5]
Tamás Vicsek,et al.
Scaling of the active zone in the Eden process on percolation networks and the ballistic deposition model
,
1985
.
[6]
Zhang,et al.
Dynamic scaling of growing interfaces.
,
1986,
Physical review letters.
[7]
Sander,et al.
Ballistic deposition on surfaces.
,
1986,
Physical review. A, General physics.
[8]
Stauffer,et al.
Simulation of large Eden clusters.
,
1986,
Physical review. A, General physics.