9 research outputs found
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 for all temperatures and a lattice size L=16. Through a
least-square fit we determine the critical exponents and . 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 . Accordingly with other simulations
we find . 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