8,379 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
-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
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
The Glassy Potts Model
We introduce a Potts model with quenched, frustrated disorder, that enjoys of
a gauge symmetry that forbids spontaneous magnetization, and allows the glassy
phase to extend from down to T=0. We study numerical the 4 dimensional
model with states. We show the existence of a glassy phase, and we
characterize it by studying the probability distributions of an order
parameter, the binder cumulant and the divergence of the overlap
susceptibility. We show that the dynamical behavior of the system is
characterized by aging.Comment: 4 pages including 4 (color) ps figures (all on page 4
Liquid-glass transition in equilibrium
We show in numerical simulations that a system of two coupled replicas of a
binary mixture of hard spheres undergoes a phase transition in equilibrium at a
density slightly smaller than the glass transition density for an unreplicated
system. This result is in agreement with the theories that predict that such a
transition is a precursor of the standard ideal glass transition. The critical
properties are compatible with those of an Ising system. The relations of this
approach to the conventional approach based on configurational entropy are
briefly discussed.Comment: 5 pages, 3 figures, version accepted for publication in the Physical
Review
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
Support for the value 5/2 for the spin glass lower critical dimension at zero magnetic field
We study numerically various properties of the free energy barriers in the
Edwards-Anderson model of spin glasses in the low-temperature region both in
three and four spatial dimensions. In particular, we investigated the
dependence of height of free energy barriers on system size and on the distance
between the initial and final states (i.e. the overlap distance). A related
quantity is the distribution of large local fluctuations of the overlap in
large three-dimensional samples at equilibrium. Our results for both quantities
(barriers and large deviations) are in agreement with the prediction obtained
in the framework of mean field theory. In addition, our result supports
as the lower critical dimension for the model.Comment: 11 pages, 4 figures. To appear in PNA
The ideal glass transition of Hard Spheres
We use the replica method to study the ideal glass transition of a liquid of
identical Hard Spheres. We obtain estimates of the configurational entropy in
the liquid phase, of the Kauzmann packing fraction, in the range 0.58--0.62,
and of the random close packing density, in the range 0.64--0.67, depending on
the approximation we use for the equation of state of the liquid. We also
compute the pair correlation function in the glassy states (i.e., dense
amorphous packings) and we find that the mean coordination number at random
close packing is equal to 6. All these results compare well with numerical
simulations and with other existing theories.Comment: 13 pages, 8 figure
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