34 research outputs found
Chaos and Universality in a Four-Dimensional Spin Glass
We present a finite size scaling analysis of Monte Carlo simulation results
on a four dimensional Ising spin glass. We study chaos with both coupling and
temperature perturbations, and find the same chaos exponent in each case. Chaos
is investigated both at the critical temperature and below where it seems to be
more efficient (larger exponent). Dimension four seems to be above the critical
dimension where chaos with temperature is no more present in the critical
region. Our results are consistent with the Gaussian and bimodal coupling
distributions being in the same universality class.Comment: 11 pages, including 6 postscript figures. Latex with revtex macro
Numerical Study of Order in a Gauge Glass Model
The XY model with quenched random phase shifts is studied by a T=0 finite
size defect energy scaling method in 2d and 3d. The defect energy is defined by
a change in the boundary conditions from those compatible with the true ground
state configuration for a given realization of disorder. A numerical technique,
which is exact in principle, is used to evaluate this energy and to estimate
the stiffness exponent . This method gives in
2d and in 3d, which are considerably larger than
previous estimates, strongly suggesting that the lower critical dimension is
less than three. Some arguments in favor of these new estimates are given.Comment: 4 pages, 2 figures, revtex. Submitted to Phys. Rev. Let
Fragility of the Free-Energy Landscape of a Directed Polymer in Random Media
We examine the sensitiveness of the free-energy landscape of a directed
polymer in random media with respect to various kinds of infinitesimally weak
perturbation including the intriguing case of temperature-chaos. To this end,
we combine the replica Bethe ansatz approach outlined in cond-mat/0112384, the
mapping to a modified Sinai model and numerically exact calculations by the
transfer-matrix method. Our results imply that for all the perturbations under
study there is a slow crossover from a weakly perturbed regime where rare
events take place to a strongly perturbed regime at larger length scales beyond
the so called overlap length where typical events take place leading to chaos,
i.e. a complete reshuffling of the free-energy landscape. Within the replica
space, the evidence for chaos is found in the factorization of the replicated
partition function induced by infinitesimal perturbations. This is the reflex
of explicit replica symmetry breaking.Comment: 29 pages, Revtex4, ps figure
Chaotic, memory and cooling rate effects in spin glasses: Is the Edwards-Anderson model a good spin glass?
We investigate chaotic, memory and cooling rate effects in the three
dimensional Edwards-Anderson model by doing thermoremanent (TRM) and AC
susceptibility numerical experiments and making a detailed comparison with
laboratory experiments on spin glasses. In contrast to the experiments, the
Edwards-Anderson model does not show any trace of re-initialization processes
in temperature change experiments (TRM or AC). A detailed comparison with AC
relaxation experiments in the presence of DC magnetic field or coupling
distribution perturbations reveals that the absence of chaotic effects in the
Edwards-Anderson model is a consequence of the presence of strong cooling rate
effects. We discuss possible solutions to this discrepancy, in particular the
smallness of the time scales reached in numerical experiments, but we also
question the validity of the Edwards-Anderson model to reproduce the
experimental results.Comment: 17 pages, 10 figures. The original version of the paper has been
split in two parts. The second part is now available as cond-mat/010224
Application of a minimum cost flow algorithm to the three-dimensional gauge glass model with screening
We study the three-dimensional gauge glass model in the limit of strong
screening by using a minimum cost flow algorithm, enabling us to obtain EXACT
ground states for systems of linear size L<=48. By calculating the domain-wall
energy, we obtain the stiffness exponent theta = -0.95+/-0.03, indicating the
absence of a finite temperature phase transition, and the thermal exponent
nu=1.05+/-0.03. We discuss the sensitivity of the ground state with respect to
small perturbations of the disorder and determine the overlap length, which is
characterized by the chaos exponent zeta=3.9+/-0.2, implying strong chaos.Comment: 4 pages RevTeX, 2 eps-figures include
Chaos in the Random Field Ising Model
The sensitivity of the random field Ising model to small random perturbations
of the quenched disorder is studied via exact ground states obtained with a
maximum-flow algorithm. In one and two space dimensions we find a mild form of
chaos, meaning that the overlap of the old, unperturbed ground state and the
new one is smaller than one, but extensive. In three dimensions the
rearrangements are marginal (concentrated in the well defined domain walls).
Implications for finite temperature variations and experiments are discussed.Comment: 4 pages RevTeX, 6 eps-figures include
Numerical study of the strongly screened vortex glass model in an external field
The vortex glass model for a disordered high-T_c superconductor in an
external magnetic field is studied in the strong screening limit. With exact
ground state (i.e. T=0) calculations we show that 1) the ground state of the
vortex configuration varies drastically with infinitesimal variations of the
strength of the external field, 2) the minimum energy of global excitation
loops of length scale L do not depend on the strength of the external field,
however 3) the excitation loops themself depend sensibly on the field. From 2)
we infer the absence of a true superconducting state at any finite temperature
independent of the external field.Comment: 6 pages RevTeX, 5 eps-figures include
Domain-Wall Free-Energy of Spin Glass Models:Numerical Method and Boundary Conditions
An efficient Monte Carlo method is extended to evaluate directly domain-wall
free-energy for randomly frustrated spin systems. Using the method, critical
phenomena of spin-glass phase transition is investigated in 4d +/-J Ising model
under the replica boundary condition. Our values of the critical temperature
and exponent, obtained by finite-size scaling, are in good agreement with those
of the standard MC and the series expansion studies. In addition, two
exponents, the stiffness exponent and the fractal dimension of the domain wall,
which characterize the ordered phase, are obtained. The latter value is larger
than d-1, indicating that the domain wall is really rough in the 4d Ising spin
glass phase.Comment: 9 pages Latex(Revtex), 8 eps figure
Phase-coherence threshold and vortex-glass state in diluted Josephson-junction arrays in a magnetic field
We study numerically the interplay of phase coherence and vortex-glass state
in two-dimensional Josephson-junction arrays with average rational values of
flux quantum per plaquette and random dilution of junctions. For ,
we find evidence of a phase coherence threshold value , below the
percolation concentration of diluted junctions , where the superconducting
transition vanishes. For the array behaves as a
zero-temperature vortex glass with nonzero linear resistance at finite
temperatures. The zero-temperature critical currents are insensitive to
variations in in the vortex glass region while they are strongly
dependent in the phase coherent region.Comment: 6 pages, 4 figures, to appear in Phys. Rev.
Static chaos and scaling behaviour in the spin-glass phase
We discuss the problem of static chaos in spin glasses. In the case of
magnetic field perturbations, we propose a scaling theory for the spin-glass
phase. Using the mean-field approach we argue that some pure states are
suppressed by the magnetic field and their free energy cost is determined by
the finite-temperature fixed point exponents. In this framework, numerical
results suggest that mean-field chaos exponents are probably exact in finite
dimensions. If we use the droplet approach, numerical results suggest that the
zero-temperature fixed point exponent is very close to
. In both approaches is the lower critical dimension in
agreement with recent numerical simulations.Comment: 28 pages + 6 figures, LateX, figures uuencoded at the end of fil