6,692 research outputs found
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
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
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
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
Interfaces and Lower Critical Dimension in a Spin Glass Model
In this paper we try to estimate the lower critical dimension for replica
symmetry breaking in spin glasses through the calculation of the additional
free-energy required to create a domain wall between two different phases. This
mechanism alone would say that replica symmetry would be restored at the lower
critical dimension .Comment: 14 pages, LaTeX, NORDITA preprint 94/2
On Spin-Glass Complexity
We study the quenched complexity in spin-glass mean-field models satisfying
the Becchi-Rouet-Stora-Tyutin supersymmetry. The outcome of such study,
consistent with recent numerical results, allows, in principle, to conjecture
the absence of any supersymmetric contribution to the complexity in the
Sherrington-Kirkpatrick model. The same analysis can be applied to any model
with a Full Replica Symmetry Breaking phase, e.g. the Ising -spin model
below the Gardner temperature. The existence of different solutions, breaking
the supersymmetry, is also discussed.Comment: 4 pages, 2 figures; Text changed in some parts, typos corrected,
Refs. [17],[21] and [22] added, two Refs. remove
A Numerical Study of Ultrametricity in Finite Dimensional Spin Glasses
We use a constrained Monte Carlo technique to analyze ultrametric features of
a 4 dimensional Edwards-Anderson spin glass with quenched couplings J=\pm 1. We
find that in the large volume limit an ultrametric structure emerges quite
clearly in the overlap of typical equilibrium configurations.Comment: 8 one column pages, latex, 4 figures with epsfig.st
On the number of metastable states in spin glasses
In this letter, we show that the formulae of Bray and Moore for the average
logarithm of the number of metastable states in spin glasses can be obtained by
calculating the partition function with coupled replicas with the symmetry
among these explicitly broken according to a generalization of the `two-group'
ansatz. This equivalence allows us to find solutions of the BM equations where
the lower `band-edge' free energy equals the standard static free energy. We
present these results for the Sherrington-Kirkpatrick model, but we expect them
to apply to all mean-field spin glasses.Comment: 6 pages, LaTeX, no figures. Postscript directly available
http://chimera.roma1.infn.it/index_papers_complex.htm
Numerical estimate of finite size corrections to the free energy of the SK model using Guerra--Toninelli interpolation
I use an interpolating formula introduced by Guerra and Toninelli to
investigate numerically the finite size corrections to the free energy of the
Sherrington--Kirkpatrick model. The results are compatible with a behavior at , as predicted by Parisi, Ritort and Slanina, and
a behavior below
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