---
_id: '33344'
abstract:
- lang: eng
text: The hard disk model is a 2D Gibbsian process of particles interacting via
pure hard core repulsion. At high particle density the model is believed to show
orientational order, however, it is known not to exhibit positional order. Here
we investigate to what extent particle positions may fluctuate. We consider a
finite volume version of the model in a box of dimensions 2n × 2n with arbitrary
boundary configuration, and we show that the mean square displacement of particles
near the center of the box is bounded from below by c log n. The result generalizes
to a large class of models with fairly arbitrary interaction.
author:
- first_name: Thomas
full_name: Richthammer, Thomas
id: '62054'
last_name: Richthammer
citation:
ama: Richthammer T. Lower Bound on the Mean Square Displacement of Particles in
the Hard Disk Model. *Communications in Mathematical Physics *. 2016;345:1077-1099.
doi:https://link.springer.com/article/10.1007/s00220-016-2584-0
apa: Richthammer, T. (2016). Lower Bound on the Mean Square Displacement of Particles
in the Hard Disk Model. *Communications in Mathematical Physics *, *345*,
1077–1099. https://link.springer.com/article/10.1007/s00220-016-2584-0
bibtex: '@article{Richthammer_2016, title={Lower Bound on the Mean Square Displacement
of Particles in the Hard Disk Model}, volume={345}, DOI={https://link.springer.com/article/10.1007/s00220-016-2584-0},
journal={Communications in Mathematical Physics }, author={Richthammer, Thomas},
year={2016}, pages={1077–1099} }'
chicago: 'Richthammer, Thomas. “Lower Bound on the Mean Square Displacement of Particles
in the Hard Disk Model.” *Communications in Mathematical Physics * 345 (2016):
1077–99. https://link.springer.com/article/10.1007/s00220-016-2584-0.'
ieee: 'T. Richthammer, “Lower Bound on the Mean Square Displacement of Particles
in the Hard Disk Model,” *Communications in Mathematical Physics *, vol.
345, pp. 1077–1099, 2016, doi: https://link.springer.com/article/10.1007/s00220-016-2584-0.'
mla: Richthammer, Thomas. “Lower Bound on the Mean Square Displacement of Particles
in the Hard Disk Model.” *Communications in Mathematical Physics *, vol.
345, 2016, pp. 1077–99, doi:https://link.springer.com/article/10.1007/s00220-016-2584-0.
short: T. Richthammer, Communications in Mathematical Physics 345 (2016) 1077–1099.
date_created: 2022-09-13T08:01:29Z
date_updated: 2022-09-13T08:01:36Z
department:
- _id: '96'
doi: https://link.springer.com/article/10.1007/s00220-016-2584-0
intvolume: ' 345'
language:
- iso: eng
page: 1077-1099
publication: 'Communications in Mathematical Physics '
publication_status: published
status: public
title: Lower Bound on the Mean Square Displacement of Particles in the Hard Disk Model
type: journal_article
user_id: '85821'
volume: 345
year: '2016'
...