The Glassy Potts Model

We introduce a Potts model with quenched, frustrated disorder, that enjoys of a gauge symmetry that forbids spontaneous magnetization, and allows the glassy phase to extend from $T_c$ down to T=0. We study numerical the 4 dimensional model with $q=4$ states. We show the existence of a glassy phase, and we characterize it by studying the probability distributions of an order parameter, the binder cumulant and the divergence of the overlap susceptibility. We show that the dynamical behavior of the system is characterized by aging.Comment: 4 pages including 4 (color) ps figures (all on page 4

Sequential evacuation strategy for multiple rooms toward the same means of egress

This paper examines different evacuation strategies for systems where several rooms evacuate trough the same means of egress, using microscopic pedestrian simulation.As a case study, a medium-rise office building is considered. It was found that the standard strategy, whereby the simultaneous evacuation of all levels is performed, can be improved by a sequential evacuation, beginning with the lowest floor and continuing successively with each one of the upper floors after a certain delay. The importance of the present research is that it provides the basis for the design and implementation of new evacuation strategies and alarm systems that could significantly improve the evacuation of multiple rooms trough a common means of escape.Comment: 8 pages, 4 figure

A variational approach to Ising spin glasses in finite dimensions

We introduce a hierarchical class of approximations of the random Ising spin glass in $d$ dimensions. The attention is focused on finite clusters of spins where the action of the rest of the system is properly taken into account. At the lower level (cluster of a single spin) our approximation coincides with the SK model while at the highest level it coincides with the true $d$-dimensional system. The method is variational and it uses the replica approach to spin glasses and the Parisi ansatz for the order parameter. As a result we have rigorous bounds for the quenched free energy which become more and more precise when larger and larger clusters are considered.Comment: 16 pages, Plain TeX, uses Harvmac.tex, 4 ps figures, submitted to J. Phys. A: Math. Ge

DD-dimensional Arrays of Josephson Junctions, Spin Glasses and qq-deformed Harmonic Oscillators

We study the statistical mechanics of a $D$-dimensional array of Josephson junctions in presence of a magnetic field. In the high temperature region the thermodynamical properties can be computed in the limit $D \to \infty$, where the problem is simplified; this limit is taken in the framework of the mean field approximation. Close to the transition point the system behaves very similar to a particular form of spin glasses, i.e. to gauge glasses. We have noticed that in this limit the evaluation of the coefficients of the high temperature expansion may be mapped onto the computation of some matrix elements for the $q$-deformed harmonic oscillator

On the high density behavior of Hamming codes with fixed minimum distance

We discuss the high density behavior of a system of hard spheres of diameter d on the hypercubic lattice of dimension n, in the limit n -> oo, d -> oo, d/n=delta. The problem is relevant for coding theory. We find a solution to the equations describing the liquid up to very large values of the density, but we show that this solution gives a negative entropy for the liquid phase when the density is large enough. We then conjecture that a phase transition towards a different phase might take place, and we discuss possible scenarios for this transition. Finally we discuss the relation between our results and known rigorous bounds on the maximal density of the system.Comment: 15 pages, 6 figure

Holographic dark energy described at the Hubble length

We consider holographic cosmological models of dark energy in which the infrared cutoff is set by the Hubble's radius. We show that any interacting dark energy model with a matter like term able to alleviate the coincidence problem (i.e., with a positive interaction term, regardless of its detailed form) can be recast as a noninteracting model in which the holographic parameter evolves slowly with time. Two specific cases are analyzed. First, the interacting model presented in [1] is considered, and its corresponding noninteracting version found. Then, a new noninteracting model, with a specific expression of the time-dependent holographic parameter, is proposed and analyzed along with its corresponding interacting version. We constrain the parameters of both models using observational data, and show that they can be told apart at the perturbative level.Comment: 15 pages, 6 figure

Replica Symmetry Breaking in the Random Replicant Model

We study the statistical mechanics of a model describing the coevolution of species interacting in a random way. We find that at high competition replica symmetry is broken. We solve the model in the approximation of one step replica symmetry breaking and we compare our findings with accurate numerical simulations.Comment: 12 pages, TeX, 5 postscript figures are avalaible upon request, submitted to Journal of Physics A: Mathematical and Genera

Slow Dynamics in Glasses

We will review some of the theoretical progresses that have been recently done in the study of slow dynamics of glassy systems: the general techniques used for studying the dynamics in the mean field approximation and the emergence of a pure dynamical transition in some of these systems. We show how the results obtained for a random Hamiltonian may be also applied to a given Hamiltonian. These two results open the way to a better understanding of the glassy transition in real systems