2015/04/30 by Thomas Richthammer · 6 citations
Materials Science · Mathematics · Physics and Astronomy · #Boundary (topology) #Bounded function #Class (philosophy) #Displacement (psychology) #Hard core #Material Dynamics and Properties #Mean squared displacement #Particle (ecology) #Square (algebra) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Upper and lower bounds #math-ph #math.MP #math.PR #msc:60K35 #msc:82B21 #msc:82B31
paper · pdf · doi:10.1007/s00220-016-2584-0
published in Communications in Mathematical Physics 345(3), 1077-1099 (Springer Science+Business Media) · 25 pages. The final publication of this article is available at Springer via http://dx.doi.org/10.1007/s00220-016-2584-0
openalex publication_date 2016/02/22 · arxiv created 2016/06/16 · arxiv updated 2016/06/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.