525 research outputs found
General properties of overlap probability distributions in disordered spin systems. Toward Parisi ultrametricity
For a very general class of probability distributions in disordered Ising
spin systems, in the thermodynamical limit, we prove the following property for
overlaps among real replicas. Consider the overlaps among s replicas. Add one
replica s+1. Then, the overlap q(a,s+1) between one of the first s replicas,
let us say a, and the added s+1 is either independent of the former ones, or it
is identical to one of the overlaps q(a,b), with b running among the first s
replicas, excluding a. Each of these cases has equal probability 1/s.Comment: LaTeX2e, 11 pages. Submitted to Journal of Physics A: Mathematical
and General. Also available at
http://rerumnatura.zool.su.se/stefano/ms/ghigu.p
Opinion and community formation in coevolving networks
In human societies opinion formation is mediated by social interactions,
consequently taking place on a network of relationships and at the same time
influencing the structure of the network and its evolution. To investigate this
coevolution of opinions and social interaction structure we develop a dynamic
agent-based network model, by taking into account short range interactions like
discussions between individuals, long range interactions like a sense for
overall mood modulated by the attitudes of individuals, and external field
corresponding to outside influence. Moreover, individual biases can be
naturally taken into account. In addition the model includes the opinion
dependent link-rewiring scheme to describe network topology coevolution with a
slower time scale than that of the opinion formation. With this model
comprehensive numerical simulations and mean field calculations have been
carried out and they show the importance of the separation between fast and
slow time scales resulting in the network to organize as well-connected small
communities of agents with the same opinion.Comment: 10 pages, 5 figures. New inset for Fig. 1 and references added.
Submitted to Physical Review
Comparison of the Spherical Averaged Pseudopotential Model with the Stabilized Jellium Model
We compare Kohn-Sham results (density, cohesive energy, size and effect of
charging) of the Spherical Averaged Pseudopotential Model with the Stabilized
Jellium Model for clusters of sodium and aluminum with less than 20 atoms. We
find that the Stabilized Jellium Model, although conceptually and practically
more simple, gives better results for the cohesive energy and the elastic
stiffness. We use the Local Density Approximation as well as the Generalized
Gradient Approximation to the exchange and correlation energies.Comment: 13 pages, latex, 8 figures, compressed postscript version available
at http://www.fis.uc.pt/~vieir
A Monte Carlo study of Inverse Symmetry Breaking
We make a Monte Carlo study of the coupled two-scalar
model in four dimensions at finite temperature. We
find no trace of Inverse Symmetry Breaking for values of the renormalized
parameters for which perturbation theory predicts this phenomenon.Comment: 4 pages, revtex, 3 figures include
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 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
Study of the phase transition in the 3d Ising spin glass from out of equilibrium numerical simulations
Using the decay of the out equilibrium spin-spin correlation function we
compute the equilibrium Edward-Anderson order parameter in the three
dimensional binary Ising spin glass in the spin glass phase. We have checked
that the Edward-Anderson order parameter computed from out of equilibrium
numerical simulations follows with good precision the critical law as
determined in experiments and in numerical studies at equilibrium. We have also
studied the dependence of the order parameter with the lattice size. Finally we
present a large time study of the scaling of the off-equilibrium
fluctuation-dissipation relations.Comment: 14 pages, 7 Postscript figure
Phase Transition of XY Model in Heptagonal Lattice
We numerically investigate the nature of the phase transition of the XY model
in the heptagonal lattice with the negative curvature, in comparison to other
interaction structures such as a flat two-dimensional (2D) square lattice and a
small-world network. Although the heptagonal lattice has a very short
characteristic path length like the small-world network structure, it is
revealed via calculation of the Binder's cumulant that the former exhibits a
zero-temperature phase transition while the latter has the finite-temperature
transition of the mean-field nature. Through the computation of the vortex
density as well as the correlation function in the low-temperature
approximation, we show that the absence of the phase transition originates from
the strong spinwave-type fluctuation, which is discussed in relation to the
usual 2D XY model.Comment: 5 pages, 6 figures, to be published in Europhys. Let
Matching microscopic and macroscopic responses in glasses
We first reproduce on the Janus and Janus II computers a milestone experiment
that measures the spin-glass coherence length through the lowering of
free-energy barriers induced by the Zeeman effect. Secondly we determine the
scaling behavior that allows a quantitative analysis of a new experiment
reported in the companion Letter [S. Guchhait and R. Orbach, Phys. Rev. Lett.
118, 157203 (2017)]. The value of the coherence length estimated through the
analysis of microscopic correlation functions turns out to be quantitatively
consistent with its measurement through macroscopic response functions.
Further, non-linear susceptibilities, recently measured in glass-forming
liquids, scale as powers of the same microscopic length.Comment: 6 pages, 4 figure
The Mpemba effect in spin glasses is a persistent memory effect
The Mpemba effect occurs when a hot system cools faster than an initially
colder one, when both are refrigerated in the same thermal reservoir. Using the
custom built supercomputer Janus II, we study the Mpemba effect in spin glasses
and show that it is a non-equilibrium process, governed by the coherence length
\xi of the system. The effect occurs when the bath temperature lies in the
glassy phase, but it is not necessary for the thermal protocol to cross the
critical temperature. In fact, the Mpemba effect follows from a strong
relationship between the internal energy and \xi that turns out to be a
sure-tell sign of being in the glassy phase. Thus, the Mpemba effect presents
itself as an intriguing new avenue for the experimental study of the coherence
length in supercooled liquids and other glass formers.Comment: Version accepted for publication in PNAS. 6 pages, 7 figure
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