Dynamical critical exponents for the mean-field Potts glass

In this paper we study the critical behaviour of the fully-connected p-colours Potts model at the dynamical transition. In the framework of Mode Coupling Theory (MCT), the time autocorrelation function displays a two step relaxation, with two exponents governing the approach to the plateau and the exit from it. Exploiting a relation between statics and equilibrium dynamics which has been recently introduced, we are able to compute the critical slowing down exponents at the dynamical transition with arbitrary precision and for any value of the number of colours p. When available, we compare our exact results with numerical simulations. In addition, we present a detailed study of the dynamical transition in the large p limit, showing that the system is not equivalent to a random energy model.Comment: 10 pages, 3 figure

Relaxation processes and entropic traps in the Backgammon model

We examine the density-density correlation function in a model recently proposed to study the effect of entropy barriers in glassy dynamics. We find that the relaxation proceeds in two steps with a fast beta process followed by alpha relaxation. The results are physically interpreted in the context of an adiabatic approximation which allows to separate the two processes, and to define an effective temperature in the off-equilibrium dynamics of the model. We investigate the behavior of the response function associated to the density, and find violations of the fluctuation dissipation theorem.Comment: 4 Pages including 3 Figures, Revte

Intermittency of glassy relaxation and the emergence of a non-equilibrium spontaneous measure in the aging regime

We consider heat exchange processes between non-equilibrium aging systems (in their activated regime) and the thermal bath in contact. We discuss a scenario where two different heat exchange processes concur in the overall heat dissipation: a stimulated fast process determined by the temperature of the bath and a spontaneous intermittent process determined by the fact that the system has been prepared in a non-equilibrium state. The latter is described by a probability distribution function (PDF) that has an exponential tail of width given by a parameter $\lambda$, and satisfies a fluctuation theorem (FT) governed by that parameter. The value of $\lambda$ is proportional to the so-called effective temperature, thereby providing a practical way to experimentally measure it by analyzing the PDF of intermittent events.Comment: Latex file, 8 pages + 5 postscript figure

On the correlation function of the characteristic polynomials of the hermitian Wigner ensemble

We consider the asymptotics of the correlation functions of the characteristic polynomials of the hermitian Wigner matrices $H_n=n^{-1/2}W_n$. We show that for the correlation function of any even order the asymptotic coincides with this for the GUE up to a factor, depending only on the forth moment of the common probability law $Q$ of entries $\Im W_{jk}$, $\Re W_{jk}$, i.e. that the higher moments of $Q$ do not contribute to the above limit.Comment: 20

DYNAMICAL SOLUTION OF A MODEL WITHOUT ENERGY BARRIERS

In this note we study the dynamics of a model recently introduced by one of us, that displays glassy phenomena in absence of energy barriers. Using an adiabatic hypothesis we derive an equation for the evolution of the energy as a function of time that describes extremely well the glassy behaviour observed in Monte Carlo simulations.Comment: 11 pages, LaTeX, 3 uuencoded figure

Jamming transition in granular media: A mean field approximation and numerical simulations

In order to study analytically the nature of the jamming transition in granular material, we have considered a cavity method mean field theory, in the framework of a statistical mechanics approach, based on Edwards' original idea. For simplicity we have applied the theory to a lattice model and a transition with exactly the same nature of the glass transition in mean field models for usual glass formers is found. The model is also simulated in three dimensions under tap dynamics and a jamming transition with glassy features is observed. In particular two step decays appear in the relaxation functions and dynamic heterogeneities resembling ones usually observed in glassy systems. These results confirm early speculations about the connection between the jamming transition in granular media and the glass transition in usual glass formers, giving moreover a precise interpretation of its nature.Comment: 11 pages, 12 figure

Evidence of a Critical time in Constrained Kinetic Ising models

We study the relaxational dynamics of the one-spin facilitated Ising model introduced by Fredrickson and Andersen. We show the existence of a critical time which separates an initial regime in which the relaxation is exponentially fast and aging is absent from a regime in which relaxation becomes slow and aging effects are present. The presence of this fast exponential process and its associated critical time is in agreement with some recent experimental results on fragile glasses.Comment: 20 Pages + 7 Figures, Revte

Limiting dynamics for spherical models of spin glasses at high temperature

We analyze the coupled non-linear integro-differential equations whose solutions is the thermodynamical limit of the empirical correlation and response functions in the Langevin dynamics for spherical p-spin disordered mean-field models. We provide a mathematically rigorous derivation of their FDT solution (for the high temperature regime) and of certain key properties of this solution, which are in agreement with earlier derivations based on physical grounds

Phase diagram of glassy systems in an external field

We study the mean-field phase diagram of glassy systems in a field pointing in the direction of a metastable state. We find competition among a ``magnetized'' and a ``disordered'' phase, that are separated by a coexistence line as in ordinary first order phase transitions. The coexistence line terminates in a critical point, which in principle can be observed in numerical simulations of glassy models.Comment: 4 pages, 5 figure

Glassy Mean-Field Dynamics of the Backgammon model

In this paper we present an exact study of the relaxation dynamics of the backgammon model. This is a model of a gas of particles in a discrete space which presents glassy phenomena as a result of {\it entropy barriers} in configuration space. The model is simple enough to allow for a complete analytical treatment of the dynamics in infinite dimensions. We first derive a closed equation describing the evolution of the occupation number probabilities, then we generalize the analysis to the study the autocorrelation function. We also consider possible variants of the model which allow to study the effect of energy barriers.Comment: 21 pages, revtex, 4 uuencoded figure