3,723 research outputs found
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
Replica analysis of partition-function zeros in spin-glass models
We study the partition-function zeros in mean-field spin-glass models. We
show that the replica method is useful to find the locations of zeros in a
complex parameter plane. For the random energy model, we obtain the phase
diagram in the plane and find that there are two types of distribution of
zeros: two-dimensional distribution within a phase and one-dimensional one on a
phase boundary. Phases with a two-dimensional distribution are characterized by
a novel order parameter defined in the present replica analysis. We also
discuss possible patterns of distributions by studying several systems.Comment: 23 pages, 12 figures; minor change
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
Magnetic field chaos in the SK Model
We study the Sherrington--Kirkpatrick model, both above and below the De
Almeida Thouless line, by using a modified version of the Parallel Tempering
algorithm in which the system is allowed to move between different values of
the magnetic field h. The behavior of the probability distribution of the
overlap between two replicas at different values of the magnetic field h_0 and
h_1 gives clear evidence for the presence of magnetic field chaos already for
moderate system sizes, in contrast to the case of temperature chaos, which is
not visible on system sizes that can currently be thermalized.Comment: Latex, 16 pages including 20 postscript figure
The Wandering Exponent of a One-Dimensional Directed Polymer in a Random Potential with Finite Correlation Radius
We consider a one-dimensional directed polymer in a random potential which is
characterized by the Gaussian statistics with the finite size local
correlations. It is shown that the well-known Kardar's solution obtained
originally for a directed polymer with delta-correlated random potential can be
applied for the description of the present system only in the high-temperature
limit. For the low temperature limit we have obtained the new solution which is
described by the one-step replica symmetry breaking. For the mean square
deviation of the directed polymer of the linear size L it provides the usual
scaling with the wandering exponent z = 2/3 and the
temperature-independent prefactor.Comment: 14 pages, Late
Analysis of the infinity-replica symmetry breaking solution of the Sherrington-Kirkpatrick model
In this work we analyse the Parisi's infinity-replica symmetry breaking
solution of the Sherrington - Kirkpatrick model without external field using
high order perturbative expansions. The predictions are compared with those
obtained from the numerical solution of the infinity-replica symmetry breaking
equations which are solved using a new pseudo-spectral code which allows for
very accurate results. With this methods we are able to get more insight into
the analytical properties of the solutions. We are also able to determine
numerically the end-point x_{max} of the plateau of q(x) and find that lim_{T
--> 0} x_{max}(T) > 0.5.Comment: 15 pages, 11 figures, RevTeX 4.
Large Deviations of the Free-Energy in Diluted Mean-Field Spin-Glass
Sample-to-sample free energy fluctuations in spin-glasses display a markedly
different behaviour in finite-dimensional and fully-connected models, namely
Gaussian vs. non-Gaussian. Spin-glass models defined on various types of random
graphs are in an intermediate situation between these two classes of models and
we investigate whether the nature of their free-energy fluctuations is Gaussian
or not. It has been argued that Gaussian behaviour is present whenever the
interactions are locally non-homogeneous, i.e. in most cases with the notable
exception of models with fixed connectivity and random couplings . We confirm these expectation by means of various analytical
results. In particular we unveil the connection between the spatial
fluctuations of the populations of populations of fields defined at different
sites of the lattice and the Gaussian nature of the free-energy fluctuations.
On the contrary on locally homogeneous lattices the populations do not
fluctuate over the sites and as a consequence the small-deviations of the free
energy are non-Gaussian and scales as in the Sherrington-Kirkpatrick model
Slow Dynamics in Glasses
We will review some of the theoretical progresses that have been recently
done in the study of slow dynamics of glassy systems: the general techniques
used for studying the dynamics in the mean field approximation and the
emergence of a pure dynamical transition in some of these systems. We show how
the results obtained for a random Hamiltonian may be also applied to a given
Hamiltonian. These two results open the way to a better understanding of the
glassy transition in real systems
Directed polymers on a Cayley tree with spatially correlated disorder
In this paper we consider directed walks on a tree with a fixed branching
ratio K at a finite temperature T. We consider the case where each site (or
link) is assigned a random energy uncorrelated in time, but correlated in the
transverse direction i.e. within the shell. In this paper we take the
transverse distance to be the hierarchical ultrametric distance, but other
possibilities are discussed. We compute the free energy for the case of
quenched disorder and show that there is a fundamental difference between the
case of short range spatial correlations of the disorder which behaves
similarly to the non-correlated case considered previously by Derrida and Spohn
and the case of long range correlations which has a totally different overlap
distribution which approaches a single delta function about q=1 for large L,
where L is the length of the walk. In the latter case the free energy is not
extensive in L for the intermediate and also relevant range of L values,
although in the true thermodynamic limit extensivity is restored. We identify a
crossover temperature which grows with L, and whenever T<T_c(L) the system is
always in the low temperature phase. Thus in the case of long-ranged
correlation as opposed to the short-ranged case a phase transition is absent.Comment: 23 pages, 1 figure, standard latex. J. Phys. A, accepted for
publicatio
Non-perturbative phenomena in the three-dimensional random field Ising model
The systematic approach for the calculations of the non-perturbative
contributions to the free energy in the ferromagnetic phase of the random field
Ising model is developed. It is demonstrated that such contributions appear due
to localized in space instanton-like excitations. It is shown that away from
the critical region such instanton solutions are described by the set of the
mean-field saddle-point equations for the replica vector order parameter, and
these equations can be formally reduced to the only saddle-point equation of
the pure system in dimensions (D-2). In the marginal case, D=3, the
corresponding non-analytic contribution is computed explicitly. Nature of the
phase transition in the three-dimensional random field Ising model is
discussed.Comment: 12 page
- …