Voronoi chains, blocks, and clusters in perturbed square lattices

Emanuel A. Lazar, Amir Shoan

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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.

Original languageEnglish
Article number103204
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number10
StatePublished - 22 Oct 2020

Bibliographical note

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  • exact results
  • random geometry
  • random/ordered microstructure


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