English

Voronoi chains, blocks, and clusters in perturbed square lattices

Statistical Mechanics 2020-10-27 v1 Disordered Systems and Neural Networks

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.

Keywords

Cite

@article{arxiv.2010.12962,
  title  = {Voronoi chains, blocks, and clusters in perturbed square lattices},
  author = {Emanuel A. Lazar and Amir Shoan},
  journal= {arXiv preprint arXiv:2010.12962},
  year   = {2020}
}

Comments

15 pages, 7 figures

R2 v1 2026-06-23T19:37:15.093Z