Numerical study of the transition of the four dimensional Random Field Ising Model

We study numerically the region above the critical temperature of the four dimensional Random Field Ising Model. Using a cluster dynamic we measure the connected and disconnected magnetic susceptibility and the connected and disconnected overlap susceptibility. We use a bimodal distribution of the field with $h_R=0.35T$ for all temperatures and a lattice size L=16. Through a least-square fit we determine the critical exponents $\gamma$ and $\bar{\gamma}$. We find the magnetic susceptibility and the overlap susceptibility diverge at two different temperatures. This is coherent with the existence of a glassy phase above $T_c$. Accordingly with other simulations we find $\bar{\gamma}=2\gamma$. In this case we have a scaling theory with two indipendet critical exponentsComment: 10 pages, 2 figures, Late

The overlap parameter across an inverse first order phase transition in a 3D spin-glass

We investigate the thermodynamic phase transition taking place in the Blume-Capel model in presence of quenched disorder in three dimensions (3D). In particular, performing Exchange Montecarlo simulations, we study the behavior of the order parameters accross the first order phase transition and its related coexistence region. This transition is an Inverse Freezing.Comment: 9 pages, 6 figures, Contribution to the XII International Workshop on Complex System

The random Blume-Capel model on cubic lattice: first order inverse freezing in a 3D spin-glass system

We present a numerical study of the Blume-Capel model with quenched disorder in 3D. The phase diagram is characterized by spin-glass/paramagnet phase transitions of both first and second order in the thermodynamic sense. Numerical simulations are performed using the Exchange-Monte Carlo algorithm, providing clear evidence for inverse freezing. The main features at criticality and in the phase coexistence region are investigated. The whole inverse freezing transition appears to be first order. The second order transition appears to be in the same universality class of the Edwards-Anderson model. The nature of the spin-glass phase is analyzed by means of the finite size scaling behavior of the overlap distribution functions and the four-spins real-space correlation functions. Evidence for a replica symmetry breaking-like organization of states is provided.Comment: 18 pages, 24 figures, 7 table

Spin Glasses on the Hypercube

We present a mean field model for spin glasses with a natural notion of distance built in, namely, the Edwards-Anderson model on the diluted D-dimensional unit hypercube in the limit of large D. We show that finite D effects are strongly dependent on the connectivity, being much smaller for a fixed coordination number. We solve the non trivial problem of generating these lattices. Afterwards, we numerically study the nonequilibrium dynamics of the mean field spin glass. Our three main findings are: (i) the dynamics is ruled by an infinite number of time-sectors, (ii) the aging dynamics consists on the growth of coherent domains with a non vanishing surface-volume ratio, and (iii) the propagator in Fourier space follows the p^4 law. We study as well finite D effects in the nonequilibrium dynamics, finding that a naive finite size scaling ansatz works surprisingly well.Comment: 14 pages, 22 figure

On the high-density expansion for Euclidean Random Matrices

Diagrammatic techniques to compute perturbatively the spectral properties of Euclidean Random Matrices in the high-density regime are introduced and discussed in detail. Such techniques are developed in two alternative and very different formulations of the mathematical problem and are shown to give identical results up to second order in the perturbative expansion. One method, based on writing the so-called resolvent function as a Taylor series, allows to group the diagrams in a small number of topological classes, providing a simple way to determine the infrared (small momenta) behavior of the theory up to third order, which is of interest for the comparison with experiments. The other method, which reformulates the problem as a field theory, can instead be used to study the infrared behaviour at any perturbative order.Comment: 29 page

Vibrational spectrum of topologically disordered systems

The topological nature of the disorder of glasses and supercooled liquids strongly affects their high-frequency dynamics. In order to understand its main features, we analytically studied a simple topologically disordered model, where the particles oscillate around randomly distributed centers, interacting through a generic pair potential. We present results of a resummation of the perturbative expansion in the inverse particle density for the dynamic structure factor and density of states. This gives accurate results for the range of densities found in real systems.Comment: Completely rewritten version, accepted in Physical Review Letter