Solid on Solid Model for Surface Growth in 2+1 Dimensions

Details Solid on Solid Model for Surface Growth in 2+1 Dimensions Solid on Solid Model for Surface Growth in 2+1 Dimensions

2010-01-26

arxiv.org/abs/1001.4596v1

Physica B: Condensed Matter, Volume 405, Issue 8, Pages 2072-2077 (2010)

Physics

Condensed Matter

Statistical Mechanics

13 pages, 7 figures and 1 table, Accepted for publication in Physica B: Condensed Matter

Scientific paper

10.1016/j.physb.2010.01.105

We analyze in detail the Solid-On-Solid model (SOS) 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 model (RSOS)- 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 behaviour of the SOS model in 2+1 dimensions for approximately $S\geq S_{\times}\sim 8$ belongs to the two different universality classes: during the initial time stage, $t< t_{\times}$ it belongs to the Random-Deposition (RD) class, while for $t_{\times}

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