A Study of Activated Processes in Soft Sphere Glass

On the basis of long simulations of a binary mixture of soft spheres just below the glass transition, we make an exploratory study of the activated processes that contribute to the dynamics. We concentrate on statistical measures of the size of the activated processes.Comment: 17 pages, 9 postscript figures with epsf, uses harvmac.te

Some non perturbative calculations on spin glasses

Models of spin glasses are studied with a phase transition discontinuous in the Parisi order parameter. It is assumed that the leading order corrections to the thermodynamic limit of the high temperature free energy are due to the existence of a metastable saddle point in the replica formalism. An ansatz is made on the form of the metastable point and its contribution to the free energy is calculated. The Random Energy Model is considered along with the p-spin and the p-state Potts Models in their p < infinity expansion.Comment: 12 pages, LaTe

A tentative Replica Study of the Glass Transition

We propose a method to study quantitatively the glass transition in a system of interacting particles. In spite of the absence of any quenched disorder, we introduce a replicated version of the hypernetted chain equations. The solution of these equations, for hard or soft spheres, signals a transition to the glass phase. However the predicted value of the energy and specific heat in the glass phase are wrong, calling for an improvement of this method.Comment: 9 pages, four postcript figures attache

A Search for Fluctuation-Dissipation Theorem Violations in Spin-Glasses from Susceptibility Data

We propose an indirect way of studying the fluctuation-dissipation relation in spin-glasses that only uses available susceptibility data. It is based on a dynamic extension of the Parisi-Toulouse approximation and a Curie-Weiss treatment of the average magnetic couplings. We present the results of the analysis of several sets of experimental data obtained from various samples.Comment: 7 pages, 4 figure

Generic two-phase coexistence in nonequilibrium systems

Gibbs' phase rule states that two-phase coexistence of a single-component system, characterized by an n-dimensional parameter-space, may occur in an n-1-dimensional region. For example, the two equilibrium phases of the Ising model coexist on a line in the temperature-magnetic-field phase diagram. Nonequilibrium systems may violate this rule and several models, where phase coexistence occurs over a finite (n-dimensional) region of the parameter space, have been reported. The first example of this behaviour was found in Toom's model [Toom,Geoff,GG], that exhibits generic bistability, i.e. two-phase coexistence over a finite region of its two-dimensional parameter space (see Section 1). In addition to its interest as a genuine nonequilibrium property, generic multistability, defined as a generalization of bistability, is both of practical and theoretical relevance. In particular, it has been used recently to argue that some complex structures appearing in nature could be truly stable rather than metastable (with important applications in theoretical biology), and as the theoretical basis for an error-correction method in computer science (see [GG,Gacs] for an illuminating and pedagogical discussion of these ideas).Comment: 7 pages, 6 figures, to appear in Eur. Phys. J. B, svjour.cls and svepj.clo neede

Power-law running of the effective gluon mass

The dynamically generated effective gluon mass is known to depend non-trivially on the momentum, decreasing sufficiently fast in the deep ultraviolet, in order for the renormalizability of QCD to be preserved. General arguments based on the analogy with the constituent quark masses, as well as explicit calculations using the operator-product expansion, suggest that the gluon mass falls off as the inverse square of the momentum, relating it to the gauge-invariant gluon condensate of dimension four. In this article we demonstrate that the power-law running of the effective gluon mass is indeed dynamically realized at the level of the non-perturbative Schwinger-Dyson equation. We study a gauge-invariant non-linear integral equation involving the gluon self-energy, and establish the conditions necessary for the existence of infrared finite solutions, described in terms of a momentum-dependent gluon mass. Assuming a simplified form for the gluon propagator, we derive a secondary integral equation that controls the running of the mass in the deep ultraviolet. Depending on the values chosen for certain parameters entering into the Ansatz for the fully-dressed three-gluon vertex, this latter equation yields either logarithmic solutions, familiar from previous linear studies, or a new type of solutions, displaying power-law running. In addition, it furnishes a non-trivial integral constraint, which restricts significantly (but does not determine fully) the running of the mass in the intermediate and infrared regimes. The numerical analysis presented is in complete agreement with the analytic results obtained, showing clearly the appearance of the two types of momentum-dependence, well-separated in the relevant space of parameters. Open issues and future directions are briefly discussed.Comment: 37 pages, 5 figure

Dynamical Behaviour of Low Autocorrelation Models

We have investigated the nature of the dynamical behaviour in low autocorrelation binary sequences. These models do have a glass transition $T_G$ of a purely dynamical nature. Above the glass transition the dynamics is not fully ergodic and relaxation times diverge like a power law $\tau\sim (T-T_G)^{-\gamma}$ with $\gamma$ close to $2$. Approaching the glass transition the relaxation slows down in agreement with the first order nature of the dynamical transition. Below the glass transition the system exhibits aging phenomena like in disordered spin glasses. We propose the aging phenomena as a precise method to determine the glass transition and its first order nature.Comment: 19 pages + 14 figures, LateX, figures uuencoded at the end of the fil