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Long-range orientational order of random near-lattice hard sphere and hard disk processes

Part of: Equilibrium statistical mechanics Special processes

Published online by Cambridge University Press:  16 July 2020

Alexisz Tamás Gaál
Alexisz Tamás Gaál*
Affiliation:
Courant Institute of Mathematical Sciences
*
*Postal address: 251 Mercer Street, New York, NY 10012, USA. E-mail: gaal@cims.nyu.edu
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Abstract

We show that a point process of hard spheres exhibits long-range orientational order. This process is designed to be a random perturbation of a three-dimensional lattice that satisfies a specific rigidity property; examples include the FCC and HCP lattices. We also define two-dimensional near-lattice processes by local geometry-dependent hard disk conditions. Earlier results about the existence of long-range orientational order carry over, and we obtain the existence of infinite-volume measures on two-dimensional point configurations that turn out to follow the orientation of a fixed triangular lattice arbitrarily closely.

Keywords

spontaneous symmetry breakinghard spherehard diskrigidity estimate

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 82B21: Continuum models (systems of particles, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 57 , Issue 2 , June 2020 , pp. 559 - 577
Copyright
© Applied Probability Trust 2020

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