On the absence of the glass transition in two dimensional hard disks

2007/01/05 by Marco Tarzia, M. Tarzia, Tarzia, M.
Materials Science · Mathematics · Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Material Dynamics and Properties #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech

paper · pdf · doi:10.48550/arxiv.cond-mat/0701097

Accepted for publication on JSTAT

arxiv created 2007/01/05 · openalex publication_date 2007/01/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study the glass transition in a model of identical hard spheres, focusing on the two dimensional case. In the mean-field limit the model exhibits an ideal glass transition of the same nature of that found in discontinuous spin glasses. Nevertheless, a systematic expansion around the mean-field solution seems to indicate that the glass transitions is smeared out in two dimensions, in agreement with some recent results. Our investigation could be generalized to higher spatial dimensions, providing a way to determine the lower critical dimensionality of the mean-field ideal glass picture.

Related

• Liquid, Glass and Crystal in Two-dimensional Hard disks
• On the nature of the spin glass transition
• The Geometry behind the Glass Transition and Frictional Jamming in Systems of Two-Dimensional Hard Disks
• Glass transition and random packing in the hard sphere system
• The Glass Transition of Quantum Hard Spheres in High Dimensions