9,619 research outputs found
About the ergodic regime in the analogical Hopfield neural networks. Moments of the partition function
In this paper we introduce and exploit the real replica approach for a
minimal generalization of the Hopfield model, by assuming the learned patterns
to be distributed accordingly to a standard unit Gaussian. We consider the high
storage case, when the number of patterns is linearly diverging with the number
of neurons. We study the infinite volume behavior of the normalized momenta of
the partition function. We find a region in the parameter space where the free
energy density in the infinite volume limit is self-averaging around its
annealed approximation, as well as the entropy and the internal energy density.
Moreover, we evaluate the corrections to their extensive counterparts with
respect to their annealed expressions. The fluctuations of properly introduced
overlaps, which act as order parameters, are also discussed.Comment: 15 page
How glassy are neural networks?
In this paper we continue our investigation on the high storage regime of a
neural network with Gaussian patterns. Through an exact mapping between its
partition function and one of a bipartite spin glass (whose parties consist of
Ising and Gaussian spins respectively), we give a complete control of the whole
annealed region. The strategy explored is based on an interpolation between the
bipartite system and two independent spin glasses built respectively by
dichotomic and Gaussian spins: Critical line, behavior of the principal
thermodynamic observables and their fluctuations as well as overlap
fluctuations are obtained and discussed. Then, we move further, extending such
an equivalence beyond the critical line, to explore the broken ergodicity phase
under the assumption of replica symmetry and we show that the quenched free
energy of this (analogical) Hopfield model can be described as a linear
combination of the two quenched spin-glass free energies even in the replica
symmetric framework
The Spectral Function for Finite Nuclei in the Local Density Approximation
The spectral function for finite nuclei is computed within the framework of
the Local Density Approximation, starting from nuclear matter spectral
functions obtained with a realistic nucleon-nucleon interaction. The spectral
function is decomposed into a single-particle part and a ''correlated'' part;
the latter is treated in the local density approximation.
As an application momentum distributions, quasi-particle strengths and
overlap functions for valence hole states, and the light-cone momentum
distribution in finite nuclei are computed.Comment: 21 pages + 9 figures available upon request, RevTex, preprint
KVI-108
Interpolating the Sherrington-Kirkpatrick replica trick
The interpolation techniques have become, in the past decades, a powerful
approach to lighten several properties of spin glasses within a simple
mathematical framework. Intrinsically, for their construction, these schemes
were naturally implemented into the cavity field technique, or its variants as
the stochastic stability or the random overlap structures. However the first
and most famous approach to mean field statistical mechanics with quenched
disorder is the replica trick. Among the models where these methods have been
used (namely, dealing with frustration and complexity), probably the best known
is the Sherrington-Kirkpatrick spin glass: In this paper we are pleased to
apply the interpolation scheme to the replica trick framework and test it
directly to the cited paradigmatic model: interestingly this allows to obtain
easily the replica-symmetric control and, synergically with the broken replica
bounds, a description of the full RSB scenario, both coupled with several minor
theorems. Furthermore, by treating the amount of replicas as an
interpolating parameter (far from its original interpretation) this can be
though of as a quenching temperature close to the one introduce in
off-equilibrium approaches and, within this viewpoint, the proof of the
attended commutativity of the zero replica and the infinite volume limits can
be obtained.Comment: This article is dedicated to David Sherrington on the occasion of his
seventieth birthda
General properties of overlap probability distributions in disordered spin systems. Toward Parisi ultrametricity
For a very general class of probability distributions in disordered Ising
spin systems, in the thermodynamical limit, we prove the following property for
overlaps among real replicas. Consider the overlaps among s replicas. Add one
replica s+1. Then, the overlap q(a,s+1) between one of the first s replicas,
let us say a, and the added s+1 is either independent of the former ones, or it
is identical to one of the overlaps q(a,b), with b running among the first s
replicas, excluding a. Each of these cases has equal probability 1/s.Comment: LaTeX2e, 11 pages. Submitted to Journal of Physics A: Mathematical
and General. Also available at
http://rerumnatura.zool.su.se/stefano/ms/ghigu.p
Spin Glass Computations and Ruelle's Probability Cascades
We study the Parisi functional, appearing in the Parisi formula for the
pressure of the SK model, as a functional on Ruelle's Probability Cascades
(RPC). Computation techniques for the RPC formulation of the functional are
developed. They are used to derive continuity and monotonicity properties of
the functional retrieving a theorem of Guerra. We also detail the connection
between the Aizenman-Sims-Starr variational principle and the Parisi formula.
As a final application of the techniques, we rederive the Almeida-Thouless line
in the spirit of Toninelli but relying on the RPC structure.Comment: 20 page
On the Thermodynamic Limit in Random Resistors Networks
We study a random resistors network model on a euclidean geometry \bt{Z}^d.
We formulate the model in terms of a variational principle and show that, under
appropriate boundary conditions, the thermodynamic limit of the dissipation per
unit volume is finite almost surely and in the mean. Moreover, we show that for
a particular thermodynamic limit the result is also independent of the boundary
conditions.Comment: 14 pages, LaTeX IOP journal preprint style file `ioplppt.sty',
revised version to appear in Journal of Physics
Temperature dependence of the volume and surface contributions to the nuclear symmetry energy within the coherent density fluctuation model
The temperature dependence of the volume and surface components of the
nuclear symmetry energy (NSE) and their ratio is investigated in the framework
of the local density approximation (LDA). The results of these quantities for
finite nuclei are obtained within the coherent density fluctuation model
(CDFM). The CDFM weight function is obtained using the temperature-dependent
proton and neutron densities calculated through the HFBTHO code that solves the
nuclear Skyrme-Hartree-Fock-Bogoliubov problem by using the cylindrical
transformed deformed harmonic-oscillator basis. We present and discuss the
values of the volume and surface contributions to the NSE and their ratio
obtained for the Ni, Sn, and Pb isotopic chains around double-magic Ni,
Sn, and Pb nuclei. The results for the -dependence of the
considered quantities are compared with estimations made previously for zero
temperature showing the behavior of the NSE components and their ratio, as well
as with the available experimental data. The sensitivity of the results on
various forms of the density dependence of the symmetry energy is studied. We
confirm the existence of `kinks' of these quantities as functions of the mass
number at MeV for the double closed-shell nuclei Ni and Sn
and the lack of `kinks' for the Pb isotopes, as well as the disappearance of
these kinks as the temperature increases.Comment: 14 pages, 12 figures, 1 table, accepted for publication in Physical
Review
Classical Rotons in Cold Atomic Traps
We predict the emergence of a roton minimum in the dispersion relation of
elementary excitations in cold atomic gases in the presence of diffusive light.
In large magneto-topical traps, multiple-scattering of light is responsible for
the collective behavior of the system, which is associated to an effective
Coulomb-like interaction between the atoms. In optically thick clouds, the
re-scattered light undergoes diffusive propagation, which is responsible for a
stochastic short-range force acting on the atoms. We show that the dynamical
competition between these two forces results on a new polariton mode, which
exhibits a roton minimum. Making use of Feynman's formula for the static
structure factor, we show that the roton minimum is related to the appearance
of long-range order in the system.Comment: 5 pages, 3 figure
The Boltzmann Equation in Scalar Field Theory
We derive the classical transport equation, in scalar field theory with a
V(phi) interaction, from the equation of motion for the quantum field. We
obtain a very simple, but iterative, expression for the effective action which
generates all the n-point Green functions in the high-temperature limit. An
explicit closed form is given in the static case.Comment: 10 pages, using RevTeX (corrected TeX misprints
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