597 research outputs found
Bell's Jump Process in Discrete Time
The jump process introduced by J. S. Bell in 1986, for defining a quantum
field theory without observers, presupposes that space is discrete whereas time
is continuous. In this letter, our interest is to find an analogous process in
discrete time. We argue that a genuine analog does not exist, but provide
examples of processes in discrete time that could be used as a replacement.Comment: 7 pages LaTeX, no figure
Phase Transition in Ferromagnetic Ising Models with Non-Uniform External Magnetic Fields
In this article we study the phase transition phenomenon for the Ising model
under the action of a non-uniform external magnetic field. We show that the
Ising model on the hypercubic lattice with a summable magnetic field has a
first-order phase transition and, for any positive (resp. negative) and bounded
magnetic field, the model does not present the phase transition phenomenon
whenever , where is the external
magnetic field.Comment: 11 pages. Published in Journal of Statistical Physics - 201
Potts models in the continuum. Uniqueness and exponential decay in the restricted ensembles
In this paper we study a continuum version of the Potts model. Particles are
points in R^d, with a spin which may take S possible values, S being at least
3. Particles with different spins repel each other via a Kac pair potential. In
mean field, for any inverse temperature there is a value of the chemical
potential at which S+1 distinct phases coexist. For each mean field pure phase,
we introduce a restricted ensemble which is defined so that the empirical
particles densities are close to the mean field values. Then, in the spirit of
the Dobrushin Shlosman theory, we get uniqueness and exponential decay of
correlations when the range of the interaction is large enough. In a second
paper, we will use such a result to implement the Pirogov-Sinai scheme proving
coexistence of S+1 extremal DLR measures.Comment: 72 pages, 1 figur
Concentration inequalities for random fields via coupling
We present a new and simple approach to concentration inequalities for
functions around their expectation with respect to non-product measures, i.e.,
for dependent random variables. Our method is based on coupling ideas and does
not use information inequalities. When one has a uniform control on the
coupling, this leads to exponential concentration inequalities. When such a
uniform control is no more possible, this leads to polynomial or
stretched-exponential concentration inequalities. Our abstract results apply to
Gibbs random fields, in particular to the low-temperature Ising model which is
a concrete example of non-uniformity of the coupling.Comment: New corrected version; 22 pages; 1 figure; New result added:
stretched-exponential inequalit
Versatile module for experiments with focussing neutron guides
We report the development of a versatile module that permits fast and
reliable use of focussing neutron guides under varying scattering angles. A
simple procedure for setting up the module and neutron guides is illustrated by
typical intensity patterns to highlight operational aspects as well as typical
parasitic artefacts. Combining a high-precision alignment table with separate
housings for the neutron guides on kinematic mounts, the change-over between
neutron guides with different focussing characteristics requires no
readjustments of the experimental set-up. Exploiting substantial gain factors,
we demonstrate the performance of this versatile neutron scattering module in a
study of the effects of uniaxial stress on the domain populations in the
transverse spin density wave phase of single crystal Cr
Band structure of helimagnons in MnSi resolved by inelastic neutron scattering
A magnetic helix realizes a one-dimensional magnetic crystal with a period
given by the pitch length . Its spin-wave excitations -- the
helimagnons -- experience Bragg scattering off this periodicity leading to gaps
in the spectrum that inhibit their propagation along the pitch direction. Using
high-resolution inelastic neutron scattering the resulting band structure of
helimagnons was resolved by preparing a single crystal of MnSi in a single
magnetic-helix domain. At least five helimagnon bands could be identified that
cover the crossover from flat bands at low energies with helimagnons basically
localized along the pitch direction to dispersing bands at higher energies. In
the low-energy limit, we find the helimagnon spectrum to be determined by a
universal, parameter-free theory. Taking into account corrections to this
low-energy theory, quantitative agreement is obtained in the entire energy
range studied with the help of a single fitting parameter.Comment: 5 pages, 3 figures; (v2) slight modifications, published versio
Partially ordered models
We provide a formal definition and study the basic properties of partially
ordered chains (POC). These systems were proposed to model textures in image
processing and to represent independence relations between random variables in
statistics (in the later case they are known as Bayesian networks). Our chains
are a generalization of probabilistic cellular automata (PCA) and their theory
has features intermediate between that of discrete-time processes and the
theory of statistical mechanical lattice fields. Its proper definition is based
on the notion of partially ordered specification (POS), in close analogy to the
theory of Gibbs measure. This paper contains two types of results. First, we
present the basic elements of the general theory of POCs: basic geometrical
issues, definition in terms of conditional probability kernels, extremal
decomposition, extremality and triviality, reconstruction starting from
single-site kernels, relations between POM and Gibbs fields. Second, we prove
three uniqueness criteria that correspond to the criteria known as bounded
uniformity, Dobrushin and disagreement percolation in the theory of Gibbs
measures.Comment: 54 pages, 11 figures, 6 simulations. Submited to Journal of Stat.
Phy
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