142 research outputs found
Reply to Comment on "Triviality of the Ground State Structure in Ising Spin Glasses"
We reply to the comment of Marinari and Parisi [cond-mat/0002457 v2] on our
paper [Phys. Rev. Lett. 83, 5126 (1999) and cond-mat/9906323]. We show that the
data in the comment are affected by strong finite-size corrections. Therefore
the original conclusion of our paper still stands.Comment: Reply to comment cond-mat/0002457 on cond-mat/9906323. Final version
with minor change
Comment on ``Triviality of the Ground State Structure in Ising Spin Glasses''
We show that the evidence of cond-mat/9906323 does not discriminate among
droplet model and mean field like behavior.Comment: 1 page comment with two .ps figures included. Rewritten version, one
error correcte
Spin and link overlaps in 3-dimensional spin glasses
Excitations of three-dimensional spin glasses are computed numerically. We
find that one can flip a finite fraction of an LxLxL lattice with an O(1)
energy cost, confirming the mean field picture of a non-trivial spin overlap
distribution P(q). These low energy excitations are not domain-wall-like,
rather they are topologically non-trivial and they reach out to the boundaries
of the lattice. Their surface to volume ratios decrease as L increases and may
asymptotically go to zero. If so, link and window overlaps between the ground
state and these excited states become ``trivial''.Comment: Extra fits comparing TNT to mean field, summarized in a tabl
On the Effects of Changing the Boundary Conditions on the Ground State of Ising Spin Glasses
We compute and analyze couples of ground states of 3D spin glass systems with
the same quenched noise but periodic and anti-periodic boundary conditions for
different lattice sizes. We discuss the possible different behaviors of the
system, we analyze the average link overlap, the probability distribution of
window overlaps (among ground states computed with different boundary
conditions) and the spatial overlap and link overlap correlation functions. We
establish that the picture based on Replica Symmetry Breaking correctly
describes the behavior of 3D Spin Glasses.Comment: 25 pages with 11 ps figures include
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
The +/-J Spin Glass: Effects of Ground State Degeneracy
We perform Monte Carlo simulations of the Ising spin glass at low temperature
in three dimensions with a +/-J distribution of couplings. Our results display
crossover scaling between T=0 behavior, where the order parameter distribution
P(q) becomes trivial for L -> , and finite-T behavior, where the
non-trivial part of P(q) has a much weaker dependence on the size L, and is
possibly size independent.Comment: 4 pages, 5 figures. Replaced with published version. Minor change
Landscape of solutions in constraint satisfaction problems
We present a theoretical framework for characterizing the geometrical
properties of the space of solutions in constraint satisfaction problems,
together with practical algorithms for studying this structure on particular
instances. We apply our method to the coloring problem, for which we obtain the
total number of solutions and analyze in detail the distribution of distances
between solutions.Comment: 4 pages, 4 figures. Replaced with published versio
Nature of the Spin Glass State
The nature of the spin glass state is investigated by studying changes to the
ground state when a weak perturbation is applied to the bulk of the system. We
consider short range models in three and four dimensions and the infinite range
Sherrington-Kirkpatrick (SK) and Viana-Bray models. Our results for the SK and
Viana-Bray models agree with the replica symmetry breaking picture. The data
for the short range models fit naturally a picture in which there are large
scale excitations which cost a finite energy but whose surface has a fractal
dimension, , less than the space dimension . We also discuss a possible
crossover to other behavior at larger length scales than the sizes studied.Comment: 4 pages, 4 postscript figures included. Final version, only minor
changes mad
Domain wall entropy of the bimodal two-dimensional Ising spin glass
We report calculations of the domain wall entropy for the bimodal
two-dimensional Ising spin glass in the critical ground state. The L * L system
sizes are large with L up to 256. We find that it is possible to fit the
variance of the domain wall entropy to a power function of L. However, the
quality of the data distributions are unsatisfactory with large L > 96.
Consequently, it is not possible to reliably determine the fractal dimension of
the domain walls.Comment: 4 pages, 2 figures, submitted to PR
State Hierarchy Induced by Correlated Spin Domains in short range spin glasses
We generate equilibrium configurations for the three and four dimensional
Ising spin glass with Gaussian distributed couplings at temperatures well below
the transition temperature T_c. These states are analyzed by a recently
proposed method using clustering. The analysis reveals a hierarchical state
space structure. At each level of the hierarchy states are labeled by the
orientations of a set of correlated macroscopic spin domains. Our picture of
the low temperature phase of short range spin glasses is that of a State
Hierarchy Induced by Correlated Spin domains (SHICS). The complexity of the low
temperature phase is manifest in the fact that the composition of such a spin
domain (i.e. its constituent spins), as well as its identifying label, are
defined and determined by the ``location'' in the state hierarchy at which it
appears. Mapping out the phase space structure by means of the orientations
assumed by these domains enhances our ability to investigate the overlap
distribution, which we find to be non-trivial. Evidence is also presented that
these states may have a non-ultrametric structure.Comment: 30 pages, 17 figure
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