Universality in glassy systems

The properties of a diluted spin-glass model are reviewed. This model interpolates between a spin glass and a frustrated lattice gas which displays glassy behaviour at high density. Using the effective potential introduced by Franz and Parisi, we show in the mean-field formalism that its static properties are closely related to those of the p-spin-glass models. These models are strongly related to glass-forming liquids. In the mean-field formalism they exhibit in fact a dynamical transition described by the same equations as in the schematic mode-coupling theory. Compared to the p-spin model, the frustrated lattice gas model is more appropriate for describing a supercooled liquid, being constituted essentially of diffusing particles. Numerically in three dimensions we in fact show that the frustrated lattice gas model exhibits qualitatively the properties of glass-forming liquids. Interestingly, the diffusion coefficient exhibits a sharp crossover from a power-law behaviour at low density to a Vogel-Fulcher or Arrhenius behaviour at high density, suggesting a crossover from mode-coupling behaviour to a hopping regime.