10,769 research outputs found
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
Metastable States, Relaxation Times and Free-energy Barriers in Finite Dimensional Glassy Systems
In this note we discuss metastability in a long-but-finite range disordered
model for the glass transition. We show that relaxation is dominated by
configuration belonging to metastable states and associate an in principle
computable free-energy barrier to the equilibrium relaxation time. Adam-Gibbs
like relaxation times appear naturally in this approach.Comment: 4 pages, 2 figures. Typos correcte
First steps of a nucleation theory in disordered systems
We devise a field theoretical formalism for a microscopic theory of
nucleation processes and phase coexistence in finite dimensional glassy
systems. We study disordered -spin models with large but finite range of
interaction. We work in the framework of glassy effective potential theory
which in mean-field is a non-convex, two minima function of the overlap. We
will associate metastability and phase coexistence with the existence of space
inhomogeneous solution of suitable field equations and we will study the
simplest of such solutions.Comment: 31 pages, 4 figures. Content revised, typos correcte
Interfaces and Lower Critical Dimension in a Spin Glass Model
In this paper we try to estimate the lower critical dimension for replica
symmetry breaking in spin glasses through the calculation of the additional
free-energy required to create a domain wall between two different phases. This
mechanism alone would say that replica symmetry would be restored at the lower
critical dimension .Comment: 14 pages, LaTeX, NORDITA preprint 94/2
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
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
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
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
Two-pion exchange and strong form-factors in covariant field theories
In this work improvements to the application of the Gross equation to nuclear
systems are tested. In particular we evaluate the two pion exchange diagrams,
including the crossed-box diagram, using models developed within the
spectator-on-mass-shell covariant formalism. We found that the form factors
used in these models induce spurious contributions that violate the unitary cut
requirement. We tested then some alternative form-factors in order to preserve
the unitarity condition. With this new choice, the difference between the exact
and the spectator-on-mass-shell amplitudes is of the order of the one boson
scalar exchange, supporting the idea that this difference may be parameterized
by this type of terms.Comment: RevTeX, 21 pages, 19 figures (PostScript
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