685 research outputs found
Phase Transition in the 1d Random Field ising model with long range interaction
We study the one dimensional Ising model with ferromagnetic, long range
interaction which decays as |i-j|^{-2+a}, 1/2< a<1, in the presence of an
external random filed. we assume that the random field is given by a collection
of independent identically distributed random variables, subgaussian with mean
zero. We show that for temperature and strength of the randomness (variance)
small enough with P=1 with respect to the distribution of the random fields
there are at least two distinct extremal Gibbs measures
Translation-invariance of two-dimensional Gibbsian point processes
The conservation of translation as a symmetry in two-dimensional systems with
interaction is a classical subject of statistical mechanics. Here we establish
such a result for Gibbsian particle systems with two-body interaction, where
the interesting cases of singular, hard-core and discontinuous interaction are
included. We start with the special case of pure hard core repulsion in order
to show how to treat hard cores in general.Comment: 44 pages, 6 figure
Neighborhood radius estimation in Variable-neighborhood Random Fields
We consider random fields defined by finite-region conditional probabilities
depending on a neighborhood of the region which changes with the boundary
conditions. To predict the symbols within any finite region it is necessary to
inspect a random number of neighborhood symbols which might change according to
the value of them. In analogy to the one dimensional setting we call these
neighborhood symbols the context of the region. This framework is a natural
extension, to d-dimensional fields, of the notion of variable-length Markov
chains introduced by Rissanen (1983) in his classical paper. We define an
algorithm to estimate the radius of the smallest ball containing the context
based on a realization of the field. We prove the consistency of this
estimator. Our proofs are constructive and yield explicit upper bounds for the
probability of wrong estimation of the radius of the context
Droplet condensation and isoperimetric towers
We consider a variational problem in a planar convex domain, motivated by
statistical mechanics of crystal growth in a saturated solution. The minimizers
are constructed explicitly and are completely characterized
The low-temperature phase of Kac-Ising models
We analyse the low temperature phase of ferromagnetic Kac-Ising models in
dimensions . We show that if the range of interactions is \g^{-1},
then two disjoint translation invariant Gibbs states exist, if the inverse
temperature \b satisfies \b -1\geq \g^\k where \k=\frac
{d(1-\e)}{(2d+1)(d+1)}, for any \e>0. The prove involves the blocking
procedure usual for Kac models and also a contour representation for the
resulting long-range (almost) continuous spin system which is suitable for the
use of a variant of the Peierls argument.Comment: 19pp, Plain Te
Graded cluster expansion for lattice systems
In this paper we develop a general theory which provides a unified treatment
of two apparently different problems. The weak Gibbs property of measures
arising from the application of Renormalization Group maps and the mixing
properties of disordered lattice systems in the Griffiths' phase. We suppose
that the system satisfies a mixing condition in a subset of the lattice whose
complement is sparse enough namely, large regions are widely separated. We then
show how it is possible to construct a convergent multi-scale cluster
expansion
1-Loop improved lattice action for the nonlinear sigma-model
In this paper we show the Wilson effective action for the 2-dimensional
O(N+1)-symmetric lattice nonlinear sigma-model computed in the 1-loop
approximation for the nonlinear choice of blockspin , \Phi(x)=
\Cav\phi(x)/{|\Cav\phi(x)|},where \Cav is averaging of the fundamental field
over a square of side .
The result for is composed of the classical perfect action with a
renormalized coupling constant , an augmented contribution from a
Jacobian, and further genuine 1-loop correction terms. Our result extends
Polyakov's calculation which had furnished those contributions to the effective
action which are of order , where is the lattice spacing
of the fundamental lattice. An analytic approximation for the background field
which enters the classical perfect action will be presented elsewhere.Comment: 3 (2-column format) pages, 1 tex file heplat99.tex, 1 macro package
Espcrc2.sty To appear in Nucl. Phys. B, Proceedings Supplements Lattice 9
Energy transport in stochastically perturbed lattice dynamics
We consider lattice dynamics with a small stochastic perturbation of order
ε and prove that for a space-time scale of order \varepsilon\^-1 the local
spectral density (Wigner function) evolves according to a linear transport
equation describing inelastic collisions. For an energy and momentum conserving
chain the transport equation predicts a slow decay, as 1/\sqrt{t}, for the
energy current correlation in equilibrium. This is in agreement with previous
studies using a different method.Comment: Changed title and introductio
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