2,742 research outputs found
A conjectured scenario for order-parameter fluctuations in spin glasses
We study order-parameter fluctuations (OPF) in disordered systems by
considering the behavior of some recently introduced paramaters which
have proven very useful to locate phase transitions. We prove that both
parameters G (for disconnected overlap disorder averages) and (for
connected disorder averages) take the respective universal values 1/3 and 13/31
in the limit for any {\em finite} volume provided the ground state is
{\em unique} and there is no gap in the ground state local-field distributions,
conditions which are met in generic spin-glass models with continuous couplings
and no gap at zero coupling. This makes ideal parameters to locate
phase transitions in disordered systems much alike the Binder cumulant is for
ordered systems. We check our results by exactly computing OPF in a simple
example of uncoupled spins in the presence of random fields and the
one-dimensional Ising spin glass. At finite temperatures, we discuss in which
conditions the value 1/3 for G may be recovered by conjecturing different
scenarios depending on whether OPF are finite or vanish in the infinite-volume
limit. In particular, we discuss replica equivalence and its natural
consequence when OPF are finite. As an example of
a model where OPF vanish and replica equivalence does not give information
about G we study the Sherrington-Kirkpatrick spherical spin-glass model by
doing numerical simulations for small sizes. Again we find results compatible
with G=1/3 in the spin-glass phase.Comment: 18 pages, 9 postscript figure
On the Use of Optimized Monte Carlo Methods for Studying Spin Glasses
We start from recently published numerical data by Hatano and Gubernatis
cond-mat/0008115 to discuss properties of convergence to equilibrium of
optimized Monte Carlo methods (bivariate multi canonical and parallel
tempering). We show that these data are not thermalized, and they lead to an
erroneous physical picture. We shed some light on why the bivariate multi
canonical Monte Carlo method can fail.Comment: 6 pages, 5 eps 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
Replica Symmetry Breaking in the Random Replicant Model
We study the statistical mechanics of a model describing the coevolution of
species interacting in a random way. We find that at high competition replica
symmetry is broken. We solve the model in the approximation of one step replica
symmetry breaking and we compare our findings with accurate numerical
simulations.Comment: 12 pages, TeX, 5 postscript figures are avalaible upon request,
submitted to Journal of Physics A: Mathematical and Genera
Parisi States in a Heisenberg Spin-Glass Model in Three Dimensions
We have studied low-lying metastable states of the Heisenberg model
in two () and three () dimensions having developed a hybrid genetic
algorithm. We have found a strong evidence of the occurrence of the Parisi
states in but not in . That is, in lattices, there exist
metastable states with a finite excitation energy of for
, and energy barriers between the ground state and
those metastable states are with in
but with in . We have also found droplet-like
excitations, suggesting a mixed scenario of the replica-symmetry-breaking
picture and the droplet picture recently speculated in the Ising SG model.Comment: 4 pages, 6 figure
Equilibrium and off-equilibrium simulations of the 4d Gaussian spin glass
In this paper we study the on and off-equilibrium properties of the four
dimensional Gaussian spin glass. In the static case we determine with more
precision that in previous simulations both the critical temperature as well as
the critical exponents. In the off-equilibrium case we settle the general form
of the autocorrelation function, and show that is possible to obtain
dynamically, for the first time, a value for the order parameter.Comment: 16 pages and 13 figures, uses epsfig.sty and rotate.sty. Some minor
grammatical changes. Also available at
http://chimera.roma1.infn.it/index_papers_complex.htm
Loop expansion around the Bethe-Peierls approximation for lattice models
We develop an effective field theory for lattice models, in which the only
non-vanishing diagrams exactly reproduce the topology of the lattice. The
Bethe-Peierls approximation appears naturally as the saddle point
approximation. The corrections to the saddle-point result can be obtained
systematically. We calculate the lowest loop corrections for magnetisation and
correlation function.Comment: 8 page
On the out of equilibrium order parameters in long-range spin-glases
We show that the dynamical order parameters can be reexpressed in terms of
the distribution of the staggered auto-correlation and response functions. We
calculate these distributions for the out of equilibrium dynamics of the
Sherrington-Kirpatrick model at long times. The results suggest that the
landscape this model visits at different long times in an out of equilibrium
relaxation process is, in a sense, self-similar. Furthermore, there is a
similarity between the landscape seen out of equilibrium at long times and the
equilibrium landscape. The calculation is greatly simplified by making use of
the superspace notation in the dynamical approach. This notation also
highlights the rather mysterious formal connection between the dynamical and
replica approaches.Comment: 25 pages, Univ. di Roma I preprint #1049 (we replaced the file by the
RevTex file, figures available upon request
First-order transitions and triple point on a random p-spin interaction model
The effects of competing quadrupolar- and spin-glass orderings are
investigated on a spin-1 Ising model with infinite-range random -spin
interactions. The model is studied through the replica approach and a phase
diagram is obtained in the limit . The phase diagram, obtained
within replica-symmetry breaking, exhibits a very unusual feature in magnetic
models: three first-order transition lines meeting at a commom triple point,
where all phases of the model coexist.Comment: 9 pages, 2 ps figures include
Measuring equilibrium properties in aging systems
We corroborate the idea of a close connection between replica symmetry
breaking and aging in the linear response function for a large class of
finite-dimensional systems with short-range interactions. In these system,
characterized by a continuity condition with respect to weak random
perturbations of the Hamiltonian, the ``fluctuation dissipation ratio'' in
off-equilibrium dynamics should be equal to the static cumulative distribution
function of the overlaps. This allows for an experimental measurement of the
equilibrium order parameter function.Comment: 5 pages, LaTeX. The paper has been completely rewritten and shortene
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