10,616 research outputs found
Temperature evolution and bifurcations of metastable states in mean-field spin glasses, with connections with structural glasses
The correlations of the free-energy landscape of mean-field spin glasses at
different temperatures are investigated, concentrating on models with a first
order freezing transition. Using a ``potential function'' we follow the
metastable states of the model in temperature, and discuss the possibility of
level crossing (which we do not find) and multifurcation (which we find). The
dynamics at a given temperature starting from an equilibrium configuration at a
different temperature is also discussed. In presence of multifurcation, we find
that the equilibrium is never achieved, leading to aging behaviour at slower
energy levels than usual aging. The relevance of the observed mechanisms for
real structural glasses is discussed, and some numerical simulations of a soft
sphere model of glass are presented.Comment: 16 pages, LaTeX, 10 figures (12 postscript files
Analytic determination of dynamical and mosaic length scales in a Kac glass model
We consider a disordered spin model with multi-spin interactions undergoing a
glass transition. We introduce a dynamic and a static length scales and compute
them in the Kac limit (long--but--finite range interactions). They diverge at
the dynamic and static phase transition with exponents (respectively) -1/4 and
-1. The two length scales are approximately equal well above the mode coupling
transition. Their discrepancy increases rapidly as this transition is
approached. We argue that this signals a crossover from mode coupling to
activated dynamics.Comment: 4 pages, 4 eps figures. New version conform to the published on
Series Expansion of the Off-Equilibrium Mode Coupling Equations
We show that computing the coefficients of the Taylor expansion of the
solution of the off-equilibrium dynamical equations characterizing models with
quenched disorder is a very effective way to understand the long time
asymptotic behavior. We study the spherical spin glass model, and we
compute the asymptotic energy (in the critical region and down to ) and
the coefficients of the time decay of the energy.Comment: 9 pages, LaTeX, 3 uuencoded figure
A note on the Guerra and Talagrand theorems for Mean Field Spin Glasses: the simple case of spherical models
The aim of this paper is to discuss the main ideas of the Talagrand proof of
the Parisi Ansatz for the free-energy of Mean Field Spin Glasses with a
physicist's approach. We consider the case of the spherical -spin model,
which has the following advantages: 1) the Parisi Ansatz takes the simple ``one
step replica symmetry breaking form'', 2) the replica free-energy as a function
of the order parameters is simple enough to allow for numerical maximization
with arbitrary precision. We present the essential ideas of the proof, we
stress its connections with the theory of effective potentials for glassy
systems, and we reduce the technically more difficult part of the Talagrand's
analysis to an explicit evaluation of the solution of a variational problem.Comment: 20 pages, 5 figures. Added references and minor language correction
Exact summation of vertex corrections to the penetration depth in d-wave superconductors
A variety of experiments suggest that in the cuprates, the low-energy
superconducting quasiparticles undergo forward scattering from extended
impurity potentials. We argue that when such potentials dominate the
scattering, the penetration depth may be computed in a simple zero-angle
scattering approximation (ZSA), in which the vertex corrections to the Meissner
effect may be summed exactly. We find a remarkably simple relationship between
the normal fluid density and the quasiparticle density of states of the
disordered system which holds for every realization of the disorder. We expect
this result to be relevant to the -plane penetration depth in high-purity
single crystals of underdoped YBCO.Comment: 4 pages, submitted to PR
Basins of attraction of metastable states of the spherical -spin model
We study the basins of attraction of metastable states in the spherical
-spin spin glass model, starting the relaxation dynamics at a given distance
from a thermalized condition. Weighting the initial condition with the
Boltzmann distribution we find a finite size for the basins. On the contrary, a
white weighting of the initial condition implies vanishing basins of
attraction. We make the corresponding of our results with the ones of a
recently constructed effective potential.Comment: LaTeX, 7 pages, 7 eps figure
Switching of the vortex polarity in a magnetic nanodisk by a DC current
We study the dynamics of a vortex state nanodisk due to a dc spin current,
perpendicular to the disk plane. The irreversible switching of the vortex
polarity takes place above some threshold current. The detailed description of
these processes is obtained by spin-lattice simulations.Comment: REVTeX, 4 pages, 3 figure
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
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