Statistical Topology of Perturbed Two-Dimensional Lattices

TL;DR

This paper analyzes how small perturbations affect the Voronoi cell topologies in 2D lattices, providing analytical and numerical insights into the topological changes in models of finite-temperature crystals.

Contribution

It offers the first analytical characterization of Voronoi topology distributions in perturbed 2D lattices, bridging ideal lattice models and finite-temperature effects.

Findings

Analytical formulas for topology distributions under infinitesimal perturbations

Numerical results illustrating topology changes with finite perturbations

Insights into lattice stability and topological variability at finite temperatures

Abstract

The Voronoi cell of any atom in a lattice is identical. If atoms are perturbed from their lattice coordinates, then the topologies of the Voronoi cells of the atoms will change. We consider the distribution of Voronoi cell topologies in two-dimensional perturbed systems. These systems can be thought of as simple models of finite-temperature crystals. We give analytical results for the distribution of Voronoi topologies of points in two-dimensional Bravais lattices under infinitesimal perturbations and present a discussion with numerical results for finite perturbations.