9,378 research outputs found
On the finite size corrections to some random matching problems
We get back to the computation of the leading finite size corrections to some
random link matching problems, first adressed by Mezard and Parisi [J. Physique
48 (1987) 1451-1459]. In the so-called bipartite case, their result is in
contradiction with subsequent works. We show that they made some mistakes, and
correcting them, we get the expected result. In the non bipartite case, we
agree with their result but push the analytical treatment furtherComment: 22 pages, 3 figure
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
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 origin of ultrametricity
In this paper we show that in systems where the probability distribution of
the the overlap is non trivial in the infinity volume limit, the property of
ultrametricity can be proved in general starting from two very simple and
natural assumptions: each replica is equivalent to the others (replica
equivalence or stochastic stability) and all the mutual information about a
pair of equilibrium configurations is encoded in their mutual distance or
overlap (separability or overlap equivalence).Comment: 13 pages, 1 figur
An Improved Estimator for the Correlation Function of 2D Nonlinear Sigma Models
I present a new improved estimator for the correlation function of 2D
nonlinear sigma models. Numerical tests for the 2D XY model and the 2D
O(3)-invariant vector model were performed. For small physical volume, i.e. a
lattice size small compared to the to the bulk correlation length, a reduction
of the statistical error of the finite system correlation length by a factor of
up to 30 compared to the cluster-improved estimator was observed. This
improvement allows for a very accurate determination of the running coupling
proposed by M. L"uscher et al. for 2D O(N)-invariant vector models.Comment: 20 pages, LaTeX + 2 ps figures, CERN-TH.7375/9
Inherent Structures in m-component Spin Glasses
We observe numerically the properties of the infinite-temperature inherent
structures of m-component vector spin glasses in three dimensions. An increase
of m implies a decrease of the amount of minima of the free energy, down to the
trivial presence of a unique minimum. For little m correlations are small and
the dynamics are quickly arrested, while for larger m low-temperature
correlations crop up and the convergence is slower, to a limit that appears to
be related with the system size.Comment: Version accepted in Phys. Rev. B, 10 pages, 11 figure
A variational approach to Ising spin glasses in finite dimensions
We introduce a hierarchical class of approximations of the random Ising spin
glass in dimensions. The attention is focused on finite clusters of spins
where the action of the rest of the system is properly taken into account. At
the lower level (cluster of a single spin) our approximation coincides with the
SK model while at the highest level it coincides with the true -dimensional
system. The method is variational and it uses the replica approach to spin
glasses and the Parisi ansatz for the order parameter. As a result we have
rigorous bounds for the quenched free energy which become more and more precise
when larger and larger clusters are considered.Comment: 16 pages, Plain TeX, uses Harvmac.tex, 4 ps figures, submitted to J.
Phys. A: Math. Ge
-dimensional Arrays of Josephson Junctions, Spin Glasses and -deformed Harmonic Oscillators
We study the statistical mechanics of a -dimensional array of Josephson
junctions in presence of a magnetic field. In the high temperature region the
thermodynamical properties can be computed in the limit , where
the problem is simplified; this limit is taken in the framework of the mean
field approximation. Close to the transition point the system behaves very
similar to a particular form of spin glasses, i.e. to gauge glasses. We have
noticed that in this limit the evaluation of the coefficients of the high
temperature expansion may be mapped onto the computation of some matrix
elements for the -deformed harmonic oscillator
A numerical study of the overlap probability distribution and its sample-to-sample fluctuations in a mean-field model
In this paper we study the fluctuations of the probability distributions of
the overlap in mean field spin glasses in the presence of a magnetic field on
the De Almeida-Thouless line. We find that there is a large tail in the left
part of the distribution that is dominated by the contributions of rare
samples. Different techniques are used to examine the data and to stress on
different aspects of the contribution of rare samples.Comment: 13 pages, 11 figure
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