1-loop contribution to the dynamical exponents in spin glasses

We evaluate the corrections to the mean field values of the $x$ and the $z$ exponents at the first order in the $\epsilon$-expansion, for $T=T_c$. We find that both $x$ and $z$ are decreasing when the space dimension decreases.Comment: 12 pages 3 Postscript figure

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

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

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

SCALING AND INTERMITTENCY IN BURGERS' TURBULENCE

We use the mapping between Burgers' equation and the problem of a directed polymer in a random medium in order to study the fully developped turbulence in the $N$ dimensional forced Burgers' equation. The stirring force corresponds to a quenched (spatio temporal) random potential for the polymer. The properties of the inertial regime are deduced from a study of the directed polymer on length scales smaller than the correlation length of the potential. From this study we propose an Ansatz for the velocity field in the large Reynolds number limit of the forced Burgers' equation in $N$ dimensions. This Ansatz allows us to compute exactly the full probability distribution of the velocity difference $u(r)$ between points separated by a distance $r$ much smaller than the correlation length of the forcing. We find that the moments $$ scale as $r^{\zeta(q)}$ with $\zeta(q) \equiv 1$ for all $q \geq 1$. This strong `intermittency' is related to the large scale singularities of the velocity field, which is concentrated on a $N-1$ dimensional froth-like structure.Comment: 35 pages latex, 4 ps figures in separate uufiles package

The dynamical structure factor in disordered systems

We study the spectral width as a function of the external momentum for the dynamical structure factor of a disordered harmonic solid, considered as a toy model for supercooled liquids and glasses. Both in the context of single-link coherent potential approximation and of a single-defect approximation, two different regimes are clearly identified: if the density of states at zero energy is zero, the Rayleigh $p^4$ law is recovered for small momentum. On the contrary, if the disorder induces a non vanishing density of states at zero energy, a linear behaviour is obtained. The dynamical structure factor is numerically calculated in lattices as large as $96^3$, and satisfactorily agrees with the analytical computations.Comment: 7 pages plus 4 postscript figure

Correlation between magnetic and transport properties of phase separated La0.5_{0.5}Ca0.5_{0.5}MnO3_{3}

The effect of low magnetic fields on the magnetic and electrical transport properties of polycrystalline samples of the phase separated compound La$_{0.5}$Ca$_{0.5}$MnO$_{3}$ is studied. The results are interpreted in the framework of the field induced ferromagnetic fraction enlargement mechanism. A fraction expansion coefficient af, which relates the ferromagnetic fraction f with the applied field H, was obtained. A phenomenological model to understand the enlargement mechanism is worked out.Comment: 3 pages, 3 figures, presented at the Fifth LAW-MMM, to appear in Physica B, Minor change