1,116 research outputs found
The Fully Frustrated Hypercubic Model is Glassy and Aging at Large
We discuss the behavior of the fully frustrated hypercubic cell in the
infinite dimensional mean-field limit. In the Ising case the system undergoes a
glass transition, well described by the random orthogonal model. Under the
glass temperature aging effects show clearly. In the case there is no sign
of a phase transition, and the system is always a paramagnet.Comment: Figures added in uufiles format, and epsf include
Numerical simulations on the 4d Heisenberg spin glass
We study the 4d Heisenberg spin glass model with Gaussian nearest-neighbor
interactions. We use finite size scaling to analyze the data. We find a
behavior consistent with a finite temperature spin glass transition. Our
estimates for the critical exponents agree with the results from
epsilon-expansion.Comment: 11 pages, LaTeX, preprint ROMA1 n. 105
Reaction rate calculation by parallel path swapping
The efficiency of path sampling simulations can be improved considerably
using the approach of path swapping. For this purpose, we have devised a new
algorithmic procedure based on the transition interface sampling technique. In
the same spirit of parallel tempering, paths between different ensembles are
swapped, but the role of temperature is here played by the interface position.
We have tested the method on the denaturation transition of DNA using the
Peyrard-Bishop-Dauxois model. We find that the new algorithm gives a reduction
of the computational cost by a factor 20.Comment: 5 pages, 3 figure
Real space application of the mean-field description of spin glass dynamics
The out of equilibrium dynamics of finite dimensional spin glasses is
considered from a point of view going beyond the standard `mean-field theory'
versus `droplet picture' debate of the last decades. The main predictions of
both theories concerning the spin glass dynamics are discussed. It is shown, in
particular, that predictions originating from mean-field ideas concerning the
violations of the fluctuation-dissipation theorem apply quantitatively,
provided one properly takes into account the role of the spin glass coherence
length which plays a central role in the droplet picture. Dynamics in a uniform
magnetic field is also briefly discussed.Comment: 4 pages, 4 eps figures. v2: published versio
On the Effects of a Bulk Perturbation on the Ground State of 3D Ising Spin Glasses
We compute and analyze couples of ground states of 3D spin glasses before and
after applying a volume perturbation which adds to the Hamiltonian a repulsion
from the true ground state. The physical picture based on Replica Symmetry
Breaking is in excellent agreement with the observed behavior.Comment: 4 pages including 5 .ps figure
Finding long cycles in graphs
We analyze the problem of discovering long cycles inside a graph. We propose
and test two algorithms for this task. The first one is based on recent
advances in statistical mechanics and relies on a message passing procedure.
The second follows a more standard Monte Carlo Markov Chain strategy. Special
attention is devoted to Hamiltonian cycles of (non-regular) random graphs of
minimal connectivity equal to three
3D Spin Glass and 2D Ferromagnetic XY Model: a Comparison
We compare the probability distributions and Binder cumulants of the overlap
in the 3D Ising spin glass with those of the magnetization in the ferromagnetic
2D XY model. We analyze similarities and differences. Evidence for the
existence of a phase transition in the spin glass model is obtained thanks to
the crossing of the Binder cumulant. We show that the behavior of the XY model
is fully compatible with the Kosterlitz-Thouless scenario. Finite size effects
have to be dealt with by using great care in order to discern among two very
different physical pictures that can look very similar if analyzed without
large attention.Comment: 14 pages and 6 figures. Also available at
http://chimera.roma1.infn.it/index_papers_complex.htm
4D Spin Glasses in Magnetic Field Have a Mean Field like Phase
By using numerical simulations we show that the 4D Edwards Anderson
spin glass in magnetic field undergoes a mean field like phase transition. We
use a dynamical approach: we simulate large lattices (of volume ) and work
out the behavior of the system in limit where both and go to infinity,
but where the limit is taken first. By showing that the dynamic
overlap converges to a value smaller than the static one we exhibit replica
symmetry breaking. The critical exponents are compatible with the ones obtained
by mean field computations.Comment: Physrev format, 5 ps figures include
A Non-Disordered Glassy Model with a Tunable Interaction Range
We introduce a non-disordered lattice spin model, based on the principle of
minimizing spin-spin correlations up to a (tunable) distance R. The model can
be defined in any spatial dimension D, but already for D=1 and small values of
R (e.g. R=5) the model shows the properties of a glassy system: deep and well
separated energy minima, very slow relaxation dynamics, aging and non-trivial
fluctuation-dissipation ratio.Comment: 4 pages, 5 figure
Sample-to-sample fluctuations of power spectrum of a random motion in a periodic Sinai model
The Sinai model of a tracer diffusing in a quenched Brownian potential is a
much studied problem exhibiting a logarithmically slow anomalous diffusion due
to the growth of energy barriers with the system size. However, if the
potential is random but periodic, the regime of anomalous diffusion crosses
over to one of normal diffusion once a tracer has diffused over a few periods
of the system. Here we consider a system in which the potential is given by a
Brownian Bridge on a finite interval and then periodically repeated
over the whole real line, and study the power spectrum of the diffusive
process in such a potential. We show that for most of realizations of
in a given realization of the potential, the low-frequency behavior is
, i.e., the same as for standard Brownian motion, and
the amplitude is a disorder-dependent random variable with a finite
support. Focusing on the statistical properties of this random variable, we
determine the moments of of arbitrary, negative or positive order
, and demonstrate that they exhibit a multi-fractal dependence on , and a
rather unusual dependence on the temperature and on the periodicity , which
are supported by atypical realizations of the periodic disorder. We finally
show that the distribution of has a log-normal left tail, and
exhibits an essential singularity close to the right edge of the support, which
is related to the Lifshitz singularity. Our findings are based both on analytic
results and on extensive numerical simulations of the process .Comment: 8 pages, 5 figure
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