112 research outputs found
Crossover from - to -relaxation in cooperative facilitation dynamics
and 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 - to
- 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 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 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
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