REPLICA.bib
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@COMMENT{{Command line: bib2bib -ob REPLICA.bib -c " ropsections:'REPLICA' " bigBiblioFile.bib}}
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@COMMENT{{ concatenation of journals_ref.bib withpyblio.bib optimization.bib mypapers.bib other.bib refvulg.bib these_ref.bib philo.bib ../math/journals_ref.bib ../math/citeseer.bib ../math/books.bib }}
@COMMENT{{ date: Thu Nov 2 00:20:16 CET 2006 }}
@MISC{parisi1998replica,
AUTHOR = {Giorgio Parisi},
TITLE = {On the replica method for glassy systems},
OPTHOWPUBLISHED = {},
OPTMONTH = {},
YEAR = {1998},
NOTE = {Contribution to the Conference in Honour of Giovanni
Paladin, Rome September 1997. 10 pages and 2
figures},
ROPSECTIONS = {DISORDER REPLICA PHYSX},
PS = {/sci_docs/physics/papers/arxiv/parisi1998replica.ps.gz},
ABSTRACT = {In this talk we review our theoretical understanding
of spin glasses paying a particular attention to the
basic physical ideas. We introduce the replica
method and we describe its probabilistic
consequences (we stress the recently discovered
importance of stochastic stability). We show that
the replica method is not restricted to systems with
quenched disorder. We present the consequences on
the dynamics of the system when it slows approaches
equilibrium are presented: they are confirmed by
large scale simulations, while we are still awaiting
for a direct experimental verification.}
}
@MISC{parisi1999replica,
AUTHOR = {Giorgio Parisi},
TITLE = {Replica and Glasses},
YEAR = {1999},
NOTE = {Contribution to the NATO-ASI school on Liquid State
Theory (Patti 1998). 25 pages and 6 figures},
URL = {http://fr.arxiv.org/abs/cond-mat/9907052},
PS = {/sci_docs/physics/papers/arxiv/parisi1999replica.ps.gz},
ROPSECTIONS = {PHYSX DISORDER REPLICA},
ABSTRACT = {In these two lectures I review our theoretical
understanding of spin glasses paying a particular
attention to the basic physical ideas. We introduce
the replica method and we describe its probabilistic
consequences (we stress the recently discovered
importance of stochastic stability). We show that
the replica method is not restricted to systems with
quenched disorder. We present the consequences on
the dynamics of the system when it slows approaches
equilibrium are presented: they are confirmed by
large scale simulations, while we are still awaiting
for a direct experimental}
}
@ARTICLE{marinari2000replica,
AUTHOR = {Enzo Marinari and Giorgio Parisi },
TITLE = {Replica Symmetry Breaking in Short-Range Spin
Glasses: Theoretical Foundations and Numerical
Evidences},
JOURNAL = {Journal of Statistical Physics},
YEAR = {2000},
VOLUME = {98},
NUMBER = {5-6},
PAGES = {973-1074},
ROPSECTIONS = {PHYSX REPLICA SURVEY},
URL = {http://fr.arxiv.org/abs/cond-mat/9906076},
PS = {/sci_docs/physics/papers/arxiv/marinari1999replica.ps.gz},
PDF = {/sci_docs/physics/papers/JStatPhys/marinari2000replica.pdf},
ABSTRACT = {We discuss replica symmetry breaking (RSB) in spin
glasses. We update work in this area, from both the
analytical and numerical points of view. We give
particular attention to the difficulties stressed by
Newman and Stein concerning the problem of
constructing pure states in spin glass systems. We
mainly discuss what happens in finite-dimensional,
realistic spin glasses. Together with a detailed
review of some of the most important features,
facts, data, and phenomena, we present some new
theoretical ideas and numerical results. We discuss
among others the basic idea of the RSB theory,
correlation functions, interfaces, overlaps, pure
states, random field, and the dynamical approach. We
present new numerical results for the behaviors of
coupled replicas and about the numerical
verification of sum rules, and we review some of the
available numerical results that we consider of
larger importance (for example, the determination of
the phase transition point, the correlation
functions, the window overlaps, and the dynamical
behavior of the system).},
KEYWORDS = {disorder, state, finite volume, spin glass,
interface, replicas, symmetry breaking}
}
@ARTICLE{gyorgyi2001techniques,
AUTHOR = {G. Györgyi},
TITLE = {Techniques of replica symmetry breaking and the
storage problem of the McCulloch-Pitts neuron},
JOURNAL = {Physics Reports},
YEAR = {2001},
VOLUME = {342},
NUMBER = {4-5},
PAGES = {263-392},
MONTH = {February},
PDF = {/sci_docs/physics/papers/PhysRep/gyorgyi2001techniques.pdf},
ROPSECTIONS = {REPLICA SURVEY},
ABSTRACT = {In this article we review the framework for
spontaneous replica symmetry breaking. Subsequently
that is applied to the example of the statistical
mechanical description of the storage properties of
a McCulloch¯ Pitts neuron, i.e., simple
perceptron. It is shown that in the neuron problem,
the general formula that is at the core of all
problems admitting Parisi's replica symmetry
breaking ansatz with a one-component order parameter
appears. The details of Parisi's method are reviewed
extensively, with regard to the wide range of
systems where the method may be applied. Parisi's
partial differential equation and related
differential equations are discussed, and the Green
function technique is introduced for the calculation
of replica averages, the key to determining the
averages of physical quantities. The Green function
of the Fokker¯Planck equation due to Sompolinsky
turns out to play the role of the statistical
mechanical Green function in the graph rules for
replica correlators. The subsequently obtained graph
rules involve only tree graphs, as appropriate for a
mean-field-like model. The lowest order
Ward¯Takahashi identity is recovered analytically
and shown to lead to the Goldstone modes in
continuous replica symmetry breaking phases. The
need for a replica symmetry breaking theory in the
storage problem of the neuron has arisen due to the
thermodynamical instability of formerly given
solutions. Variational forms for the neuron's free
energy are derived in terms of the order parameter
function x(q), for different prior distribution of
synapses. Analytically in the high temperature limit
and numerically in generic cases various phases are
identified, among them is one similar to the Parisi
phase in long-range interaction spin
glasses. Extensive quantities like the error per
pattern change slightly with respect to the known
unstable solutions, but there is a significant
difference in the distribution of non-extensive
quantities like the synaptic overlaps and the
pattern storage stability parameter. A simulation
result is also reviewed and compared with the
prediction of the theory.},
KEYWORDS = {Neural networks; Pattern storage; Spin glasses;
Replica symmetry breaking}
}
@ARTICLE{panyukov1996statistical,
AUTHOR = {Sergei Panyukov and Yitzhak Rabin},
TITLE = {Statistical physics of polymer gels},
JOURNAL = {Physics Reports},
YEAR = {1996},
VOLUME = {269},
NUMBER = {1--2},
PAGES = {1-131},
MONTH = {May},
ROPSECTIONS = {PHYSX RG REPLICA POLYMER},
PDF = {/sci_docs/physics/papers/PhysRep/panyukov1996statistical.pdf}
}
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@PHDTHESIS{schreiber1997systemes,
AUTHOR = {Georg R. Schreiber},
TITLE = {Syst{\`e}mes d{\'e}sordonn{\'e}s et frustr{\'e}s:
mod{\`e}les champ moyen et probl{\`e}mes
d'optimisation combinatoire},
SCHOOL = {CEA/Saclay, SPhT},
YEAR = {1997},
ADDRESS = {UNIVERSITE PARIS SUD - PARIS XI},
MONTH = {novembre},
ROPSECTIONS = {THESIS PHYSX DISORDER REPLICA PHASE_T},
URL = {http://theses-en-ligne.ccsd.cnrs.fr/documents/archives0/00/00/08/25/index_fr.html},
PS = {/sci_docs/physics/papers/thesis/schreiber1997systemes.ps.gz},
ABSTRACT = {In the present Ph.D. dissertation I present results
concerning disordered and frustrated models of
relevance in statistical mechanics and in
combinatorial optimization. As an application of
spin glass theory I study the disordered and
frustrated Blume-Emery-Griffiths model. The model is
treated in its mean-field approximation using
replicas. Within the Ansatz of replica-symmetry, I
present a complete numerical solution; I also
discuss effects of replica symmetry breaking. The
stability of the RS solution is studied and the
regions of instability inferred. The phase diagram
exhibits first and second order transitions. The
tricritical point is still present in the frustrated
model, in agreement with former work. A version of
the BEG model with disordered chemical potential is
also studied. The calculations confirm that the
disorder decreases the tricritical
temperature. Next, I consider the graph partitioning
problem, a combinatorial optimization problem,
which, from the point of view of statistical
mechanics is a spin glass model with the constraint
of zero magnetisation. I focus on the statistical
properties of low energy solutions generated by
"heuristic" algorithms designed to solve such hard
combinatorial optimization problems. Several
heuristics proposed to solve this problem were
implemented. Scaling laws are obtained; in
particular, the average cost and its variance grow
linearly with the number of vertices of the
graphs. As a consequence the cost found by the
heuristics is self-averaging. I suggest that this
property is quite general, valid for random
solutions, quasi-optimal solutions, and probably for
the optimum solutions, too. Furthermore a ranking
method is proposed and illustrated on an ensemble of
graph partitioning problems. This ranking procedure
takes into account the quality of the solution as
well as the time necessary to find that solution. In
the third part of this dissertation I study in
detail the zero-temperatures properties of spin
glasses on sparse random graphs with fixed
connectivity. Spin glasses on these graphs may be
considered as a more realistic approximation to real
spin glasses as represented by the model of
Sherrington and Kirkpatrick. I have designed a new
algorithm for finding low energy states. Second, I
present a method for deriving the ground state
energy from heuristic algorithms, even though they
are not guaranteed to find the optimum. Third, I
present a numerical test of a conjecture due to
Banavar, Sherrington and Sourlas, giving the large
volume energy density of the ground states as
function of the connectivity. The distribution of
the order parameter is found to be non-trivial, and
I give evidence for the presence of ultrametricity
for all values of the connectivity. These results
confirm the expectation that the remarquable
properties of the infinite range
Sherrington-Kirkpatrick model carry over to more
realistic models, as for example the spin glass
model on random graphs with finite connectivity
studied in the present work. }
}
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