Crossover from β\beta- to α\alpha-relaxation in cooperative facilitation dynamics

$\beta$ and $\alpha$ relaxation processes are dynamical scaling regimes of glassy systems occurring on two separate time scales which both diverge as the glass state is approached. We study here the crossover scaling from $\beta$- to $\alpha$- relaxation in the cooperative facilitation scenario (CFS) and show that it is quantitatively described, with no adjustable parameter, by the leading order asymptotic formulas for scaling predicted by the mode-coupling theory (MCT). These results establish: (i) the mutual universality of the MCT and CFS, and (ii) the existence of a purely dynamic realization of MCT which is distinct from the well established random-first order transition scenario for disordered systems. Some implications of the emerging kinetic-static duality are discussed

The large connectivity limit of bootstrap percolation

Bootstrap percolation provides an emblematic instance of phase behavior characterised by an abrupt transition with diverging critical fluctuations. This unusual hybrid situation generally occurs in particle systems in which the occupation probability of a site depends on the state of its neighbours through a certain threshold parameter. In this paper we investigate the phase behavior of the bootstrap percolation on the regular random graph in the limit in which the threshold parameter and lattice connectivity become both increasingly large while their ratio $\alpha$ is held constant. We find that the mixed phase behavior is preserved in this limit, and that multiple transitions and higher-order bifurcation singularities occur when $\alpha$ becomes a random variable.Comment: 6 pages, 4 figure

Aging in a simple model of a structural glass

We consider a simple model of a structural glass, represented by a lattice gas with kinetic constraints in contact with a particle reservoir. Quench below the glass transition is represented by the jump of the chemical potential above a threshold. After a quench, the density approaches the critical density-where the diffusion coefficient of the particles vanishes-following a power law in time. In this regime, the two-time self-correlation functions exhibit aging. The behavior of the model can be understood in terms of simple mean-field arguments.Comment: LaTeX, 8 pages, 4 figures. Contribution to the Conference "Disorder and Chaos", Rome, September 1997. A few misprints corrected, and references update

Finite-size critical fluctuations in microscopic models of mode-coupling theory

Facilitated spin models on random graphs provide an ideal microscopic realization of the mode-coupling theory of supercooled liquids: they undergo a purely dynamic glass transition with no thermodynamic singularity. In this paper we study the fluctuations of dynamical heterogeneity and their finite-size scaling properties in the beta relaxation regime of such microscopic spin models. We compare the critical fluctuations behavior for two distinct measures of correlations with the results of a recently proposed field theoretical description based on quasi-equilibrium ideas. We find that the theoretical predictions perfectly fit the numerical simulation data once the relevant order parameter is identified with the persistence function of the spins

Testing the Edwards hypothesis in spin systems under tapping dynamics

The Edwards hypothesis of ergodicity of blocked configurations for gently tapped granular materials is tested for abstract models of spin systems on random graphs and spin chains with kinetic constraints. The tapping dynamics is modeled by considering two distinct mechanisms of energy injection: thermal and random tapping. We find that ergodicity depends upon the tapping procedure (i.e. the way the blocked configurations are dynamically accessed): for thermal tapping ergodicity is a good approximation, while it fails to describe the asymptotic stationary state reached by the random tapping dynamics.Comment: 15 pages, 8 figures. A few references adde

Equilibrium properties of the Ising frustrated lattice gas

We study the equilibrium properties of an Ising frustrated lattice gas with a mean field replica approach. This model bridges usual {\em Spin Glasses} and a version of {\em Frustrated Percolation} model, and has proven relevant to describe the glass transition. It shows a rich phase diagram which in a definite limit reduces to the known Sherrington-Kirkpatrick spin glass model.Comment: To appear in J.Physique I (september 96). All figures included in an one-page postscript fil