Long range order in a hard disk model in statistical mechanics

We model two-dimensional crystals by a configuration space in which every admissible configuration is a hard disk configuration and a perturbed version of some triangular lattice with side length one. In this model we show that, under the uniform distribution, expected configurations in a given box...

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Bibliographic Details
Published in:arXiv.org 2013-11
Main Author: Alexisz, Tamás Gaál
Format: Article
Language:English
Subjects:
Configurations
Disk drives
Hard disks
Long range order
Particle density (concentration)
Statistical mechanics
Two dimensional models
Online Access:Get full text
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Description
Summary:We model two-dimensional crystals by a configuration space in which every admissible configuration is a hard disk configuration and a perturbed version of some triangular lattice with side length one. In this model we show that, under the uniform distribution, expected configurations in a given box are arbitrarily close to some triangular lattice whenever the particle density is chosen sufficiently high. This choice can be made independent of the box size.
ISSN:2331-8422
DOI:10.48550/arxiv.1311.5523