5,977 research outputs found
Spin glass models with Kac interactions
In this paper I will review my work on disordered systems -spin glass model
with two body and body interactions- with long but finite interaction
range . I will describe the relation of these model with Mean Field Theory
in the Kac limit and some attempts to go beyond mean field.Comment: Proceedings of the Stat-phys23 conferenc
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
Standalone vertex ďŹnding in the ATLAS muon spectrometer
A dedicated reconstruction algorithm to find decay vertices in the ATLAS muon spectrometer is presented. The algorithm searches the region just upstream of or inside the muon spectrometer volume for multi-particle vertices that originate from the decay of particles with long decay paths. The performance of the algorithm is evaluated using both a sample of simulated Higgs boson events, in which the Higgs boson decays to long-lived neutral particles that in turn decay to bbar b final states, and pp collision data at âs = 7 TeV collected with the ATLAS detector at the LHC during 2011
Hiding solutions in random satisfiability problems: A statistical mechanics approach
A major problem in evaluating stochastic local search algorithms for
NP-complete problems is the need for a systematic generation of hard test
instances having previously known properties of the optimal solutions. On the
basis of statistical mechanics results, we propose random generators of hard
and satisfiable instances for the 3-satisfiability problem (3SAT). The design
of the hardest problem instances is based on the existence of a first order
ferromagnetic phase transition and the glassy nature of excited states. The
analytical predictions are corroborated by numerical results obtained from
complete as well as stochastic local algorithms.Comment: 5 pages, 4 figures, revised version to app. in PR
Glassy Mean-Field Dynamics of the Backgammon model
In this paper we present an exact study of the relaxation dynamics of the
backgammon model. This is a model of a gas of particles in a discrete space
which presents glassy phenomena as a result of {\it entropy barriers} in
configuration space. The model is simple enough to allow for a complete
analytical treatment of the dynamics in infinite dimensions. We first derive a
closed equation describing the evolution of the occupation number
probabilities, then we generalize the analysis to the study the autocorrelation
function. We also consider possible variants of the model which allow to study
the effect of energy barriers.Comment: 21 pages, revtex, 4 uuencoded figure
Domain-Wall Free-Energy of Spin Glass Models:Numerical Method and Boundary Conditions
An efficient Monte Carlo method is extended to evaluate directly domain-wall
free-energy for randomly frustrated spin systems. Using the method, critical
phenomena of spin-glass phase transition is investigated in 4d +/-J Ising model
under the replica boundary condition. Our values of the critical temperature
and exponent, obtained by finite-size scaling, are in good agreement with those
of the standard MC and the series expansion studies. In addition, two
exponents, the stiffness exponent and the fractal dimension of the domain wall,
which characterize the ordered phase, are obtained. The latter value is larger
than d-1, indicating that the domain wall is really rough in the 4d Ising spin
glass phase.Comment: 9 pages Latex(Revtex), 8 eps figure
Metastable States in Spin Glasses and Disordered Ferromagnets
We study analytically M-spin-flip stable states in disordered short-ranged
Ising models (spin glasses and ferromagnets) in all dimensions and for all M.
Our approach is primarily dynamical and is based on the convergence of a
zero-temperature dynamical process with flips of lattice animals up to size M
and starting from a deep quench, to a metastable limit. The results (rigorous
and nonrigorous, in infinite and finite volumes) concern many aspects of
metastable states: their numbers, basins of attraction, energy densities,
overlaps, remanent magnetizations and relations to thermodynamic states. For
example, we show that their overlap distribution is a delta-function at zero.
We also define a dynamics for M=infinity, which provides a potential tool for
investigating ground state structure.Comment: 34 pages (LaTeX); to appear in Physical Review
Ultrametricity in 3D Edwards-Anderson spin glasses
We perform an accurate test of Ultrametricity in the aging dynamics of the
three dimensional Edwards-Anderson spin glass. Our method consists in
considering the evolution in parallel of two identical systems constrained to
have fixed overlap. This turns out to be a particularly efficient way to study
the geometrical relations between configurations at distant large times. Our
findings strongly hint towards dynamical ultrametricity in spin glasses, while
this is absent in simpler aging systems with domain growth dynamics. A recently
developed theory of linear response in glassy systems allows to infer that
dynamical ultrametricity implies the same property at the level of equilibrium
states.Comment: 4 pages, 5 figure
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