A mean-field hard-spheres model of glass

Abstract

We present a model of spheres moving in a high-dimensional compact space. We relate it to a mixed matrix model with a $O(N)$ invariant model plus a $P(N)$ invariant perturbation. We then study the low pressure regime by performing a diagrammatic expansion of this matrix model. Finally, we show the results from numerical simulations and we present evidence for a glassy regime at high pressures.

19 pages, 5 figures included, Z-compressed postscript

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• History-Dependence and Ageing in a Periodic Long-Range Josephson Array
• Disorder-free spin glass transitions and jamming in exactly solvable mean-field models
• Minimal Potentials with Very Many Minima
• Slow dynamics of glassy systems