Glass transition in models with controlled frustration

A class of models with self-generated disorder and controlled frustration is studied. Between the trivial case, where frustration is not present at all, and the limit case, where frustration is present over every length scale, a region with local frustration is found where glassy dynamics appears. We suggest that in this region, the mean field model might undergo a p-spin like transition, and increasing the range of frustration, a crossover from a 1-step replica symmetry breaking to a continuous one might be observed.Comment: 4 pages, 6 figure

Glass transition in granular media

In the framework of schematic hard spheres lattice models for granular media we investigate the phenomenon of the ``jamming transition''. In particular, using Edwards' approach, by analytical calculations at a mean field level, we derive the system phase diagram and show that ``jamming'' corresponds to a phase transition from a ``fluid'' to a ``glassy'' phase, observed when crystallization is avoided. Interestingly, the nature of such a ``glassy'' phase turns out to be the same found in mean field models for glass formers.Comment: 7 pages, 4 figure

Stretched exponential relaxation for growing interfaces in quenched disordered media

We study the relaxation for growing interfaces in quenched disordered media. We use a directed percolation depinning model introduced by Tang and Leschhorn for 1+1-dimensions. We define the two-time autocorrelation function of the interface height C(t',t) and its Fourier transform. These functions depend on the difference of times t-t' for long enough times, this is the steady-state regime. We find a two-step relaxation decay in this regime. The long time tail can be fitted by a stretched exponential relaxation function. The relaxation time is proportional to the characteristic distance of the clusters of pinning cells in the direction parallel to the interface and it diverges as a power law. The two-step relaxation is lost at a given wave length of the Fourier transform, which is proportional to the characteristic distance of the clusters of pinning cells in the direction perpendicular to the interface. The stretched exponential relaxation is caused by the existence of clusters of pinning cells and it is a direct consequence of the quenched noise.Comment: 4 pages and 5 figures. Submitted (5/2002) to Phys. Rev.

Static and dynamic heterogeneities in irreversible gels and colloidal gelation

We compare the slow dynamics of irreversible gels, colloidal gels, glasses and spin glasses by analyzing the behavior of the so called non-linear dynamical susceptibility, a quantity usually introduced to quantitatively characterize the dynamical heterogeneities. In glasses this quantity typically grows with the time, reaches a maximum and then decreases at large time, due to the transient nature of dynamical heterogeneities and to the absence of a diverging static correlation length. We have recently shown that in irreversible gels the dynamical susceptibility is instead an increasing function of the time, as in the case of spin glasses, and tends asymptotically to the mean cluster size. On the basis of molecular dynamics simulations, we here show that in colloidal gelation where clusters are not permanent, at very low temperature and volume fractions, i.e. when the lifetime of the bonds is much larger than the structural relaxation time, the non-linear susceptibility has a behavior similar to the one of the irreversible gel, followed, at higher volume fractions, by a crossover towards the behavior of glass forming liquids.Comment: 9 pages, 3 figure