Perturbed lattices provide simple models for studying many physical systems. In this paper we study the distribution of Voronoi chains, blocks, and clusters with prescribed combinatorial features in the perturbed square lattice, generalizing earlier work. In particular, we obtain analytic results for the presence of hexagonally-ordered regions within a square-ordered phase. Connections to high-temperature crystals and to non-equilibrium phase transitions are considered. In an appendix, we briefly consider the site-percolation threshold for this system.

中文翻译：

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扰动方格中的 Voronoi 链、块和簇

微扰晶格为研究许多物理系统提供了简单的模型。在本文中，我们研究了在扰动方格中具有指定组合特征的 Voronoi 链、块和集群的分布，概括了早期的工作。特别是，我们获得了在方形有序相中存在六边形有序区域的分析结果。考虑了与高温晶体和非平衡相变的连接。在附录中，我们简要地考虑了该系统的站点渗透阈值。