Voronoi chains, blocks, and clusters in perturbed square lattices

TL;DR

This paper analyzes the structure of Voronoi chains, blocks, and clusters in perturbed square lattices, revealing insights into phase transitions and ordering phenomena relevant to physical systems.

Contribution

It generalizes previous work by providing analytic results on Voronoi structures and their relation to phase transitions in perturbed lattices.

Findings

Identification of hexagonally-ordered regions within square phases

Analytic characterization of Voronoi structures in perturbed lattices

Discussion of implications for high-temperature crystals and non-equilibrium transitions

Abstract

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.