848 research outputs found
Reply to Comment on "Ising Spin Glasses in a Magnetic Field"
The problem of the survival of a spin glass phase in the presence of a field
has been a challenging one for a long time. To date, all attempts using
equilibrium Monte Carlo methods have been unconclusive. In their comment to our
paper, Marinari, Parisi and Zuliani use out-of-equilibrium measurements to test
for an Almeida-Thouless line. In our view such a dynamic approach is not based
on very solid foundations in finite dimensional systems and so cannot be as
compelling as equilibrium approaches. Nevertheless, the results of those
authors suggests that there is a critical field near B=0.4 at zero temperature.
In view of this quite small value (compared to the mean field value), we have
reanalyzed our data. We find that if finite size scaling is to distinguish
between that small field and a zero field, we would need to go to lattice sizes
of about 20x20x20.Comment: reply to comment cond-mat/9812401 on ref. cond-mat/981141
Low T Dynamical Properties of Spin Glasses Smoothly Extrapolate to T=0
We compare ground state properties of 3D Ising Spin Glasses with Gaussian
couplings with results from off-equilibrium numerical simulations at non zero
(but low) temperatures. We find that the non-zero temperature properties of the
system smoothly connect to the T=0 behavior, confirming the point of view that
results established at T=0 typically also give relevant information about the
physics of the system.Comment: 14 pages and 4 ps figure
Numerical Simulations of the 4D Edwards-Anderson Spin Glass with Binary Couplings
We present numerical results that allow a precise determination of the
transition point and of the critical exponents of the 4D Edwards-Anderson Spin
Glass with binary quenched random couplings. We show that the low T phase
undergoes Replica Symmetry Breaking. We obtain results on large lattices, up to
a volume : we use finite size scaling to show the relevance of our
results in the infinite volume limit.Comment: 18 pages + 17 figures, revised bibliography and minor typos. Added
Journal Re
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
Make life simple: unleash the full power of the parallel tempering algorithm
We introduce a new update scheme to systematically improve the efficiency of
parallel tempering simulations. We show that by adapting the number of sweeps
between replica exchanges to the canonical autocorrelation time, the average
round-trip time of a replica in temperature space can be significantly
decreased. The temperatures are not dynamically adjusted as in previous
attempts but chosen to yield a 50% exchange rate of adjacent replicas. We
illustrate the new algorithm with results for the Ising model in two and the
Edwards-Anderson Ising spin glass in three dimensionsComment: 4 pages, 5 figure
Small Window Overlaps Are Effective Probes of Replica Symmetry Breaking in 3D Spin Glasses
We compute numerically small window overlaps in the three dimensional Edwards
Anderson spin glass. We show that they behave in the way implied by the Replica
Symmetry Breaking Ansatz, that they do not qualitatively differ from the full
volume overlap and do not tend to a trivial function when increasing the
lattice volume. On the contrary we show they are affected by small finite
volume effects, and are interesting tools for the study of the features of the
spin glass phase.Comment: 9 pages plus 5 figure
On the Phase Structure of the 3D Edwards Anderson Spin Glass
We characterize numerically the properties of the phase transition of the
three dimensional Ising spin glass with Gaussian couplings and of the low
temperature phase. We compute critical exponents on large lattices. We study in
detail the overlap probability distribution and the equilibrium overlap-overlap
correlation functions. We find a clear agreement with off-equilibrium results
from previous work. These results strongly support the existence of a
continuous spontaneous replica symmetry breaking in three dimensional spin
glasses.Comment: 30 pages and 17 figures. Final version to be published in PR
Equilibrium valleys in spin glasses at low temperature
We investigate the 3-dimensional Edwards-Anderson spin glass model at low
temperature on simple cubic lattices of sizes up to L=12. Our findings show a
strong continuity among T>0 physical features and those found previously at
T=0, leading to a scenario with emerging mean field like characteristics that
are enhanced in the large volume limit. For instance, the picture of space
filling sponges seems to survive in the large volume limit at T>0, while
entropic effects play a crucial role in determining the free-energy degeneracy
of our finite volume states. All of our analysis is applied to equilibrium
configurations obtained by a parallel tempering on 512 different disorder
realizations. First, we consider the spatial properties of the sites where
pairs of independent spin configurations differ and we introduce a modified
spin overlap distribution which exhibits a non-trivial limit for large L.
Second, after removing the Z_2 (+-1) symmetry, we cluster spin configurations
into valleys. On average these valleys have free-energy differences of O(1),
but a difference in the (extensive) internal energy that grows significantly
with L; there is thus a large interplay between energy and entropy
fluctuations. We also find that valleys typically differ by sponge-like space
filling clusters, just as found previously for low-energy system-size
excitations above the ground state.Comment: 10 pages, 8 figures, RevTeX format. Clarifications and additional
reference
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
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
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