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arXiv 1001.4596cond-mat.stat-mechcond-mat.other
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2+1维表面生长的Solid on Solid模型

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

S. Hosseinabadi, A. A. Masoudi, M. Sadegh Movahed

备注：
13 pages, 7 figures and 1 table, Accepted for publication in Physica B: Condensed Matter
发表信息：
Physica B: Condensed Matter, Volume 405, Issue 8, Pages 2072-2077 (2010)
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摘要：

我们详细分析了固体上的固体模型（SOS）的生长过程中的一个正方形衬底上的2+1维。利用马尔可夫曲面的性质，本文提出了一种确定2+1维特殊SOS模型--受限固上固模型（RSOS）粗糙度指数的方法。该模型是SOS模型，具有高度差必须为S=1的附加限制。数值结果表明，近似$S\geq S_{\times}\sim 8$的2+1维SOS模型的行为属于两个不同的普适类：在初始阶段，$t< t_{\times}$属于随机沉积（RD）类，而$t_{\times}<t\ll t_{sat}$属于Kardar-Parisi-Zhang（KPZ）普适类.交叉时间（$t_{\times}$）通过指数幂律与S相关，$1σ$置信水平下的$η=1.99\pm0.02$与参考文献\cite{e1}中报告的1+1维度相同。使用结构函数，我们计算粗糙度指数。与生长指数相反，粗糙度指数对于不同的S值不显示交叉。在一维和二维空间中，固定分离距离值与S的结构函数的标度指数分别为$ξ=0.92\pm0.05$和$ξ=0.86\pm0.05$（在$1σ$置信水平下）。

英文摘要：

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 $t_{\times}<t\ll t_{sat}$ it belongs to the Kardar-Parisi-Zhang (KPZ) universality class. The crossover time ($t_{\times}$) is related to S via a power law with exponent, $η=1.99\pm0.02$ at $1σ$ confidence level which is the same as that for 1+1 dimensions reported in Ref. \cite{e1}. Using the structure function, we compute the roughness exponent. In contrast to the growth exponent, the roughness exponent does not show crossover for different values of S. The scaling exponents of the structure function for fixed values of separation distance versus S in one and two space dimensions are $ξ=0.92\pm0.05$ and $ξ=0.86\pm0.05$ at $1σ$ confidence level, respectively.

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