arXiv 1104.05752011-04cond-mat.stat-mech

概率界面增长模型中的跃迁

Transitions in a Probabilistic Interface Growth Model

S G Alves, J G Moreira

备注：: 9 pages, 6 figures, published in JSTAT
发表信息：: J. Stat. Mech. (2011) P04022
DOI：: 10.1088/1742-5468/2011/04/P04022

摘要：

我们研究了基于概率增长规则的Wolf-Villain（WV）界面增长模型的推广。在WV模型中，粒子随机地沉积在衬底上，随后移动到结合最强的位置附近。我们引入了一个增长概率，这是成比例的网站$i$：$p_i\propto n_i^ν$的绑定数$n_i$的幂。通过大量的模拟，在$(1+1)$维中，我们发现了三种行为依赖于$ν$值：{ \it i}）如果$ν$很小，从Mullins-Hering到Edwards-Wilkinson（EW）普适性类的交叉; { \it ii}）对于$ν$的中间值，从EW到Kardar-Parisi-Zhang（KPZ）普适性类的交叉;{ \it iii}），最后，对于大的$ν$值，系统始终处于KPZ类。在$(2+1)$ -维中，我们得到三种不同的行为：{ \it i}）对于小的$ν$值，从Villain-Lai-Das Sarma到EW普适性类的交叉; { \it ii}）对于中间的$ν$值，EW类总是存在; { \it iii}）对于大的$ν$值，观察到与EW类的偏离。

英文摘要：

We study a generalization of the Wolf-Villain (WV) interface growth model based on a probabilistic growth rule. In the WV model, particles are randomly deposited onto a substrate and subsequently move to a position nearby where the binding is strongest. We introduce a growth probability which is proportional to a power of the number $n_i$ of bindings of the site $i$: $p_i\propto n_i^ν$. Through extensively simulations, in $(1+1)$-dimensions, we find three behavior depending of the $ν$ value: {\it i}) if $ν$ is small, a crossover from the Mullins-Hering to the Edwards-Wilkinson (EW) universality class; {\it ii}) for intermediate values of $ν$, a crossover from the EW to the Kardar-Parisi-Zhang (KPZ) universality class; {\it iii}) and, finally, for large $ν$ values, the system is always in the KPZ class. In $(2+1)$-dimensions, we obtain three different behaviors: {\it i}) a crossover from the Villain-Lai-Das Sarma to the EW universality class, for small $ν$ values; {\it ii}) the EW class is always present, for intermediate $ν$ values; {\it iii}) a deviation from the EW class is observed, for large $ν$ values.

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