A mean-field hard-spheres model of glass

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. Typeset using REVT E X Glassy systems can be characterized as out-of-equilibrium systems in which the relaxation is slower than the experimental time-scale [1]. The slowness of the dynamics is due to the complexity of the energy (or free-energy) landcape, which may contain a combination of barriers, bottlenecks and even flat directions. In the case of spin-glasses, the complexity of the landscape is induced by the frustration in the spin configurations, which in turn is a consequence of the (quenched) disorder in the couplings. In structural glasses the ruggedness of the landcape does not necessar...