77 research outputs found
Cluster Variation Method in Statistical Physics and Probabilistic Graphical Models
The cluster variation method (CVM) is a hierarchy of approximate variational
techniques for discrete (Ising--like) models in equilibrium statistical
mechanics, improving on the mean--field approximation and the Bethe--Peierls
approximation, which can be regarded as the lowest level of the CVM. In recent
years it has been applied both in statistical physics and to inference and
optimization problems formulated in terms of probabilistic graphical models.
The foundations of the CVM are briefly reviewed, and the relations with
similar techniques are discussed. The main properties of the method are
considered, with emphasis on its exactness for particular models and on its
asymptotic properties.
The problem of the minimization of the variational free energy, which arises
in the CVM, is also addressed, and recent results about both provably
convergent and message-passing algorithms are discussed.Comment: 36 pages, 17 figure
CVM ANALYSIS OF CROSSOVER IN THE SEMI-INFINITE ISING MODEL
The crossover behavior of the semi--infinite three dimensional Ising model is
investigated by means of Pad\'e approximant analysis of cluster variation
method results. We give estimates for ordinary critical as well as for
multicritical exponents, which are in very good agreement with extensive Monte
Carlo simulations.Comment: RevTeX, 7 pages + 2 uuencoded PostScript figures. To be published in
J. Magn. Magn. Mat. (substituted raw with encoded PostScript
Variational approximations for stochastic dynamics on graphs
We investigate different mean-field-like approximations for stochastic
dynamics on graphs, within the framework of a cluster-variational approach. In
analogy with its equilibrium counterpart, this approach allows one to give a
unified view of various (previously known) approximation schemes, and suggests
quite a systematic way to improve the level of accuracy. We compare the
different approximations with Monte Carlo simulations on a reversible
(susceptible-infected-susceptible) discrete-time epidemic-spreading model on
random graphs.Comment: 29 pages, 5 figures. Minor revisions. IOP-style
Generalized belief propagation for the magnetization of the simple cubic Ising model
A new approximation of the cluster variational method is introduced for the three-dimensional Ising model on the simple cubic lattice. The maximal cluster is, as far as we know, the largest ever used in this method. A message-passing algorithm, generalized belief propagation, is used to minimize the variational free energy. Convergence properties and performance of the algorithm are investigated. The approximation is used to compute the spontaneous magnetization, which is then compared to previous results. Using the present results as the last step in a sequence of three cluster variational approximations, an extrapolation is obtained which captures the leading critical behavior with a good accurac
Pathways of mechanical unfolding of FnIII10: Low force intermediates
We study the mechanical unfolding pathways of the domain of
fibronectin by means of an Ising--like model, using both constant force and
constant velocity protocols. At high forces and high velocities our results are
consistent with experiments and previous computational studies. Moreover, the
simplicity of the model allows us to probe the biologically relevant low force
regime, where we predict the existence of two intermediates with very close
elongations. The unfolding pathway is characterized by stochastic transitions
between these two intermediates
Kinetics of the Wako-Saito-Munoz-Eaton Model of Protein Folding
We consider a simplified model of protein folding, with binary degrees of
freedom, whose equilibrium thermodynamics is exactly solvable. Based on this
exact solution, the kinetics is studied in the framework of a local equilibrium
approach, for which we prove that (i) the free energy decreases with time, (ii)
the exact equilibrium is recovered in the infinite time limit, and (iii) the
folding rate is an upper bound of the exact one. The kinetics is compared to
the exact one for a small peptide and to Monte Carlo simulations for a longer
protein, then rates are studied for a real protein and a model structure.Comment: 4 pages, 4 figure
Six vertex model with domain-wall boundary conditions in the Bethe-Peierls approximation
We use the Bethe-Peierls method combined with the belief propagation
algorithm to study the arctic curves in the six vertex model on a square
lattice with domain-wall boundary conditions, and the six vertex model on a
rectangular lattice with partial domain-wall boundary conditions. We show that
this rather simple approximation yields results that are remarkably close to
the exact ones when these are known, and allows one to estimate the location of
the phase boundaries with relative little effort in cases in which exact
results are not available.Comment: 19 pages, 14 figure
Dynamical transition in the TASEP with Langmuir kinetics: mean-field theory
We develop a mean-field theory for the totally asymmetric simple exclusion
process (TASEP) with open boundaries, in order to investigate the so-called
dynamical transition. The latter phenomenon appears as a singularity in the
relaxation rate of the system toward its non-equilibrium steady state. In the
high-density (low-density) phase, the relaxation rate becomes independent of
the injection (extraction) rate, at a certain critical value of the parameter
itself, and this transition is not accompanied by any qualitative change in the
steady-state behavior. We characterize the relaxation rate by providing
rigorous bounds, which become tight in the thermodynamic limit. These results
are generalized to the TASEP with Langmuir kinetics, where particles can also
bind to empty sites or unbind from occupied ones, in the symmetric case of
equal binding/unbinding rates. The theory predicts a dynamical transition to
occur in this case as well.Comment: 37 pages (including 16 appendix pages), 6 figures. Submitted to
Journal of Physics
NEW TOPOLOGIES IN THE PHASE DIAGRAM OF THE SEMI-INFINITE BLUME-CAPEL MODEL
The phase diagram of the Blume--Capel model on a semi--infinite simple cubic
lattice with a (100) free surface is studied in the pair approximation of the
cluster variation method. Six main topologies are found, of which two are new,
due to the occurrence of a first order surface transition in the phase with
ordered bulk, separating two phases with large and small surface order
parameters. The latter is a new phase and is studied in some detail, giving the
behaviour of the order parameter profiles in two typical cases. A comparison is
made with the results of a low temperature expansion, where these are
available, showing a great increase in accuracy with respect to the mean field
approximation.Comment: RevTeX, 13 pages + 7 uuencoded PostScript figures (substituted raw
with encoded PostScript
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