68 research outputs found
Feynman's Propagator Applied to Network Models of Localization
Network models of dirty electronic systems are mapped onto an interacting
field theory of lower dimensionality by intepreting one space dimension as
time. This is accomplished via Feynman's interpretation of anti-particles as
particles moving backwards in time. The method developed maps calculation of
the moments of the Landauer conductance onto calculation of correlation
functions of an interacting field theory of bosons and fermions. The resulting
field theories are supersymmetric and closely related to the supersymmetric
spin-chain representations of network models recently discussed by various
authors. As an application of the method, the two-edge Chalker-Coddington model
is shown to be Anderson localized, and a delocalization transition in a related
two-edge network model (recently discussed by Balents and Fisher) is studied by
calculation of the average Landauer conductance.Comment: Latex, 14 pages, 2 fig
Finite-size scaling properties of random transverse-field Ising chains : Comparison between canonical and microcanonical ensembles for the disorder
The Random Transverse Field Ising Chain is the simplest disordered model
presenting a quantum phase transition at T=0. We compare analytically its
finite-size scaling properties in two different ensembles for the disorder (i)
the canonical ensemble, where the disorder variables are independent (ii) the
microcanonical ensemble, where there exists a global constraint on the disorder
variables. The observables under study are the surface magnetization, the
correlation of the two surface magnetizations, the gap and the end-to-end
spin-spin correlation for a chain of length . At criticality, each
observable decays typically as in both ensembles, but the
probability distributions of the rescaled variable are different in the two
ensembles, in particular in their asymptotic behaviors. As a consequence, the
dependence in of averaged observables differ in the two ensembles. For
instance, the correlation decays algebraically as 1/L in the canonical
ensemble, but sub-exponentially as in the microcanonical
ensemble. Off criticality, probability distributions of rescaled variables are
governed by the critical exponent in both ensembles, but the following
observables are governed by the exponent in the microcanonical
ensemble, instead of the exponent in the canonical ensemble (a) in the
disordered phase : the averaged surface magnetization, the averaged correlation
of the two surface magnetizations and the averaged end-to-end spin-spin
correlation (b) in the ordered phase : the averaged gap. In conclusion, the
measure of the rare events that dominate various averaged observables can be
very sensitive to the microcanonical constraint.Comment: 24 page
Contact process in a wedge
We prove that the supercritical one-dimensional contact process survives in
certain wedge-like space-time regions, and that when it survives it couples
with the unrestricted contact process started from its upper invariant measure.
As an application we show that a type of weak coexistence is possible in the
nearest-neighbor ``grass-bushes-trees'' successional model introduced in
Durrett and Swindle (1991).Comment: 11 pages, 4 figure
The Harris-Luck criterion for random lattices
The Harris-Luck criterion judges the relevance of (potentially) spatially
correlated, quenched disorder induced by, e.g., random bonds, randomly diluted
sites or a quasi-periodicity of the lattice, for altering the critical behavior
of a coupled matter system. We investigate the applicability of this type of
criterion to the case of spin variables coupled to random lattices. Their
aptitude to alter critical behavior depends on the degree of spatial
correlations present, which is quantified by a wandering exponent. We consider
the cases of Poissonian random graphs resulting from the Voronoi-Delaunay
construction and of planar, ``fat'' Feynman diagrams and precisely
determine their wandering exponents. The resulting predictions are compared to
various exact and numerical results for the Potts model coupled to these
quenched ensembles of random graphs.Comment: 13 pages, 9 figures, 2 tables, REVTeX 4. Version as published, one
figure added for clarification, minor re-wordings and typo cleanu
Random walks and polymers in the presence of quenched disorder
After a general introduction to the field, we describe some recent results
concerning disorder effects on both `random walk models', where the random walk
is a dynamical process generated by local transition rules, and on `polymer
models', where each random walk trajectory representing the configuration of a
polymer chain is associated to a global Boltzmann weight. For random walk
models, we explain, on the specific examples of the Sinai model and of the trap
model, how disorder induces anomalous diffusion, aging behaviours and Golosov
localization, and how these properties can be understood via a strong disorder
renormalization approach. For polymer models, we discuss the critical
properties of various delocalization transitions involving random polymers. We
first summarize some recent progresses in the general theory of random critical
points : thermodynamic observables are not self-averaging at criticality
whenever disorder is relevant, and this lack of self-averaging is directly
related to the probability distribution of pseudo-critical temperatures
over the ensemble of samples of size . We describe the
results of this analysis for the bidimensional wetting and for the
Poland-Scheraga model of DNA denaturation.Comment: 17 pages, Conference Proceedings "Mathematics and Physics", I.H.E.S.,
France, November 200
Finite Temperature Properties of Quantum Antiferromagnets in a Uniform Magnetic Field in One and Two Dimensions
Consider a -dimensional antiferromagnet with a quantum disordered ground
state and a gap to bosonic excitations with non-zero spin. In a finite external
magnetic field, this antiferromagnet will undergo a phase transition to a
ground state with non-zero magnetization, describable as the condensation of a
dilute gas of bosons. The finite temperature properties of the Bose gas in the
vicinity of this transition are argued to obey a hypothesis of ZERO
SCALE-FACTOR UNIVERSALITY for , with logarithmic violations in .
Scaling properties of various experimental observables are computed in an
expansion in , and exactly in .Comment: 27 pages, REVTEX 3.0, 8 Postscript figures appended, YCTP-xyz
Controversies in spine research: organ culture versus in vivo models for studies of the intervertebral disc
Intervertebral disc degeneration is a common cause of low back pain, the leading cause of disability worldwide. Appropriate preclinical models for intervertebral disc research are essential to achieving a better understanding of underlying pathophysiology and for the development, evaluation, and translation of more effective treatments. To this end, in vivo animal and ex vivo organ culture models are both widely used by spine researchers; however, the relative strengths and weaknesses of these two approaches are a source of ongoing controversy. In this article, members from the Spine and Preclinical Models Sections of the Orthopedic Research Society, including experts in both basic and translational spine research, present contrasting arguments in support of in vivo animal models versus ex vivo organ culture models for studies of the disc, supported by a comprehensive review of the relevant literature. The objective is to provide a deeper understanding of the respective advantages and limitations of these approaches, and advance the field toward a consensus with respect to appropriate model selection and implementation. We conclude that complementary use of several model types and leveraging the unique advantages of each is likely to result in the highest impact research in most instances
Workgroup report: Public health strategies for reducing aflatoxin exposure in developing countries
10.1289/ehp.9302Environmental Health Perspectives114121898-190
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