8,251 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

### $D$-dimensional Arrays of Josephson Junctions, Spin Glasses and $q$-deformed Harmonic Oscillators

We study the statistical mechanics of a $D$-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 $D \to \infty$, 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 $q$-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 $T_c$ down to T=0. We study numerical the 4 dimensional
model with $q=4$ 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

### The K-sat problem in a simple limit

We compute the thermodynamic properties of the 3-satisfiability problem in
the infinite connectivity limit. In this limit the computations can be strongly
simplified and the thermodynamical properties can be obtained with an high
accuracy. We find evidence for a continuous replica symmetry breaking in the
region of high number of clauses, $\alpha > \alpha_c$.Comment: 9 pages, 6 figures. To appear in J. Stat. Phys. Minor change

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