Spin glasses, glasses and granular materials

Abstract

Abstract The properties of a frustrated lattice gas model that combines features of spin glasses and percolation are reviewed. This model, which contains frustration as an essential ingredient, displays glassy behaviour at high densities or low temperatures and in the extreme case of quenched disorder exhibits two transitions: a percolation transition at a temperature T p and a second transition at lower temperature T 0 Numerically it is found that T p marks the onset of long-time stretched-exponential decay and the breakdown of the Stokes-Einstein relation, while T 0 coincides with the temperature where the diffusion coefficient vanishes and the nonlinear susceptibility diverges. The model is also applied to describe the complex behaviour of granular materials. The mean-field version of the model shows analogies with the mean-field version of the p-spin-glass models. These models have been much studied, since the dynamical behaviour is described by the same equations as the mode coupling theory for simple liquids.