Cluster Algorithms for Discrete Models of Colloids with Bars

S. Miracle, Dana Randall, A. Streib
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引用次数: 4

Abstract

Colloids are mixtures of two different types of molecules. The model has a hard-core constraint forcing all the molecules to occupy non-overlapping positions, but there are no additional interactions between molecules; all non-overlapping arrangements are equally likely. It is believed that colloids undergo a phase transition whereby at low density the two types of molecules will be uniformly interspersed, while at high density large clusters will form and the two types of molecules will effectively separate. While local algorithms are not believed to work at or beyond the critical point, an algorithm due to Dress and Krauth [3] offers an alternative approach to sampling potentially beyond the critical point where clusters begin to form. We study the DK algorithm on a colloid model consisting of long bars and small diamonds on the periodic lattice Z2n. We show that if we restrict the model to allow at most one bar in each column of the lattice region, then local algorithms are slow, but the DK algorithm is provably efficient (if the bars are long enough). However, we show that when we allow any number of bars per column, the DK algorithm also requires exponential time to reach equilibrium.
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带棒状胶体离散模型的聚类算法
胶体是两种不同分子的混合物。该模型有一个核心约束,迫使所有分子占据不重叠的位置,但分子之间没有额外的相互作用;所有不重叠的排列都是相等的。认为胶体发生相变,低密度时两类分子均匀分布,高密度时形成大团簇,两类分子有效分离。虽然局部算法不被认为在临界点或临界点之外工作,但Dress和Krauth[3]提出的一种算法提供了一种替代方法,可以在集群开始形成的临界点之外进行采样。研究了周期晶格Z2n上由长棒状和小菱形组成的胶体模型上的DK算法。我们表明,如果我们限制模型在晶格区域的每列中最多允许一个条,那么局部算法是缓慢的,但是DK算法是有效的(如果条足够长)。然而,我们表明,当我们允许每列有任意数量的棒时,DK算法也需要指数时间才能达到平衡。
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