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 $D_B$ of the percolation backbone to three loop order. Using renormalization group methods we obtain $D_B = 2 + \epsilon /21 - 172\epsilon^2 /9261 + 2 \epsilon^3 (- 74639 + 22680 \zeta (3))/4084101$, where $\epsilon = 6-d$ with $d$ being the spatial dimension and $\zeta (3) = 1.202057..$.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 $\chi^{(1)}$ and the mean square fluctuations of the total magnetic moment $\chi^{(2)}$ 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 $\chi^{(1)}$ and $\chi^{(2)}$. This allows us to determine the critical behavior of $\chi^{(1)}$ and $\chi^{(2)}$ 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 $\{\psi_l \}$. We calculate the family $\{\psi_l \}$ 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 $\phi$ to two-loop order. Moreover, we determine the backbone dimension $D_B$ of directed percolation clusters to two-loop order. We obtain a scaling relation for $D_B$ 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 $C_R^{(l)} (x, x^\prime)$ of the resistance between two sites x and $x^\prime$ 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 ${\psi_l}$ for the scaling behavior of the noise cumulants, $C_R^{(l)} (x, x^\prime) \sim | x - x^\prime |^{\psi_l /\nu}$, where $\nu$ 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