50 research outputs found
Multifractal current distribution in random diode networks
Recently it has been shown analytically that electric currents in a random
diode network are distributed in a multifractal manner [O. Stenull and H. K.
Janssen, Europhys. Lett. 55, 691 (2001)]. In the present work we investigate
the multifractal properties of a random diode network at the critical point by
numerical simulations. We analyze the currents running on a directed
percolation cluster and confirm the field-theoretic predictions for the scaling
behavior of moments of the current distribution. It is pointed out that a
random diode network is a particularly good candidate for a possible
experimental realization of directed percolation.Comment: RevTeX, 4 pages, 5 eps figure
The Resistance of Feynman Diagrams and the Percolation Backbone Dimension
We present a new view of Feynman diagrams for the field theory of transport
on percolation clusters. The diagrams for random resistor networks are
interpreted as being resistor networks themselves. This simplifies the field
theory considerably as we demonstrate by calculating the fractal dimension
of the percolation backbone to three loop order. Using renormalization
group methods we obtain , where with
being the spatial dimension and .Comment: 10 pages, 2 figure
Percolating granular superconductors
We investigate diamagnetic fluctuations in percolating granular
superconductors. Granular superconductors are known to have a rich phase
diagram including normal, superconducting and spin glass phases. Focusing on
the normal-superconducting and the normal-spin glass transition at low
temperatures, we study he diamagnetic susceptibility and the mean
square fluctuations of the total magnetic moment of large
clusters. Our work is based on a random Josephson network model that we analyze
with the powerful methods of renormalized field theory. We investigate the
structural properties of the Feynman diagrams contributing to the
renormalization of and . This allows us to determine
the critical behavior of and to arbitrary order in
perturbation theory.Comment: 18 pages, 2 figure
Dynamics, dynamic soft elasticity and rheology of smectic-C elastomers
We present a theory for the low-frequency, long-wavelength dynamics of soft
smectic-C elastomers with locked-in smectic layers. Our theory, which goes
beyond pure hydrodynamics, predicts a dynamic soft elasticity of these
elastomers and allows us to calculate the storage and loss moduli relevant for
rheology experiments as well as the mode structure.Comment: 4 pages, 2 figure
Multifractal properties of resistor diode percolation
Focusing on multifractal properties we investigate electric transport on
random resistor diode networks at the phase transition between the
non-percolating and the directed percolating phase. Building on first
principles such as symmetries and relevance we derive a field theoretic
Hamiltonian. Based on this Hamiltonian we determine the multifractal moments of
the current distribution that are governed by a family of critical exponents
. We calculate the family to two-loop order in a
diagrammatic perturbation calculation augmented by renormalization group
methods.Comment: 21 pages, 5 figures, to appear in Phys. Rev.
Transport on Directed Percolation Clusters
We study random lattice networks consisting of resistor like and diode like
bonds. For investigating the transport properties of these random resistor
diode networks we introduce a field theoretic Hamiltonian amenable to
renormalization group analysis. We focus on the average two-port resistance at
the transition from the nonpercolating to the directed percolating phase and
calculate the corresponding resistance exponent to two-loop order.
Moreover, we determine the backbone dimension of directed percolation
clusters to two-loop order. We obtain a scaling relation for that is in
agreement with well known scaling arguments.Comment: 4 page
Master Operators Govern Multifractality in Percolation
Using renormalization group methods we study multifractality in percolation
at the instance of noisy random resistor networks. We introduce the concept of
master operators. The multifractal moments of the current distribution (which
are proportional to the noise cumulants of the
resistance between two sites x and located on the same cluster) are
related to such master operators. The scaling behavior of the multifractal
moments is governed exclusively by the master operators, even though a myriad
of servant operators is involved in the renormalization procedure. We calculate
the family of multifractal exponents for the scaling behavior of the
noise cumulants, ,
where is the correlation length exponent for percolation, to two-loop
order.Comment: 6 page
Universal Elasticity and Fluctuations of Nematic Gels
We study elasticity of spontaneously orientationally-ordered amorphous
solids, characterized by a vanishing transverse shear modulus, as realized for
example by nematic elastomers and gels. We show that local heterogeneities and
elastic nonlinearities conspire to lead to anomalous nonlocal universal
elasticity controlled by a nontrivial infared fixed point. Namely, at long
scales, such solids are characterized by universal shear and bending moduli
that, respectively, vanish and diverge at long scales, are universally
incompressible and exhibit a universal negative Poisson ratio and a non-Hookean
elasticity down to arbitrarily low strains. Based on expansion about five
dimensions, we argue that the nematic order is stable to thermal fluctuation
and local hetergeneities down to d_lc < 3.Comment: 4 RevTeX pgs, submitted to PR