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

Weakly Coupled Motion of Individual Layers in Ferromagnetic Resonance

We demonstrate a layer- and time-resolved measurement of ferromagnetic resonance (FMR) in a Ni81Fe19 / Cu / Co93Zr7 trilayer structure. Time-resolved x-ray magnetic circular dichroism has been developed in transmission, with resonant field excitation at a FMR frequency of 2.3 GHz. Small-angle (to 0.2 degree), time-domain magnetization precession could be observed directly, and resolved to individual layers through elemental contrast at Ni, Fe, and Co edges. The phase sensitivity allowed direct measurement of relative phase lags in the precession oscillations of individual elements and layers. A weak ferromagnetic coupling, difficult to ascertain in conventional FMR measurements, is revealed in the phase and amplitude response of individual layers across resonance.Comment: 22 pages, 6 figures submitted to Physical Review

Non-perturbative renormalisation using dimensional regularisation: applications to the ε expansion

We give a prescription for the one-loop renormalisation of the imaginary parts of vertex functions in gø4, which are generated when gR \u3c 0 is non-perturbative in ɛ. This fixed point determines the imaginary parts of the critical exponents which are generated when ɛ \u3c 0, and allows us to determine the high-order behaviour of the perturbation series in E for these exponents. The generalisation of these ideas to the O(n) symmetric g(ø2)2 model is also given

Logarithmic Corrections in Dynamic Isotropic Percolation

Based on the field theoretic formulation of the general epidemic process we study logarithmic corrections to scaling in dynamic isotropic percolation at the upper critical dimension d=6. Employing renormalization group methods we determine these corrections for some of the most interesting time dependent observables in dynamic percolation at the critical point up to and including the next to leading correction. For clusters emanating from a local seed at the origin we calculate the number of active sites, the survival probability as well as the radius of gyration.Comment: 9 pages, 3 figures, version to appear in Phys. Rev.

Percolation Threshold, Fisher Exponent, and Shortest Path Exponent for 4 and 5 Dimensions

We develop a method of constructing percolation clusters that allows us to build very large clusters using very little computer memory by limiting the maximum number of sites for which we maintain state information to a number of the order of the number of sites in the largest chemical shell of the cluster being created. The memory required to grow a cluster of mass s is of the order of $s^\theta$ bytes where $\theta$ ranges from 0.4 for 2-dimensional lattices to 0.5 for 6- (or higher)-dimensional lattices. We use this method to estimate $d_{\scriptsize min}$, the exponent relating the minimum path $\ell$ to the Euclidean distance r, for 4D and 5D hypercubic lattices. Analyzing both site and bond percolation, we find $d_{\scriptsize min}=1.607\pm 0.005$ (4D) and $d_{\scriptsize min}=1.812\pm 0.006$ (5D). In order to determine $d_{\scriptsize min}$ to high precision, and without bias, it was necessary to first find precise values for the percolation threshold, $p_c$: $p_c=0.196889\pm 0.000003$ (4D) and $p_c=0.14081\pm 0.00001$ (5D) for site and $p_c=0.160130\pm 0.000003$ (4D) and $p_c=0.118174\pm 0.000004$ (5D) for bond percolation. We also calculate the Fisher exponent, $\tau$, determined in the course of calculating the values of $p_c$: $\tau=2.313\pm 0.003$ (4D) and $\tau=2.412\pm 0.004$ (5D)

Exchange narrowing of NMR line shapes in randomly diluted magnetic systems

An analysis of 19F NMR linewidths in the randomly diluted magnetic system KMnxMg1-xF3 is presented. It is shown that good agreement with measured linewidths can be obtained if in the usual asymptotic spin-diffusion assumption for the spin autocorrelation function 〈Siα(τ)Siα(0)〉avατ-d(x)/2, d(x) is taken to be independent of x above the percolation concentration. Experimental results in the system KNixMg1-xF3 are also presented. These data exhibit striking differences with the behavior of isostructural KMnxMg1-xF3 whose origin is discussed

On the relevance of percolation theory to the vulcanization transition

The relationship between vulcanization and percolation is explored from the perspective of renormalized local field theory. We show rigorously that the vulcanization and percolation correlation functions are governed by the same Gell--Mann-Low renormalization group equation. Hence, all scaling aspects of the vulcanization transition are reigned by the critical exponents of the percolation universality class.Comment: 9 pages, 2 figure

Stem cell transplantation in 40 pts with Fanconi anemia (FA): Excellent survival and low toxicity for pts with a related HLA identical donor

Univ Fed Parana, BR-80060000 Curitiba, Parana, BrazilEPM, Inst Oncol Pediat, São Paulo, BrazilEPM, Inst Oncol Pediat, São Paulo, BrazilWeb of Scienc

Diluted Networks of Nonlinear Resistors and Fractal Dimensions of Percolation Clusters

We study random networks of nonlinear resistors, which obey a generalized Ohm's law, $V\sim I^r$. Our renormalized field theory, which thrives on an interpretation of the involved Feynman Diagrams as being resistor networks themselves, is presented in detail. By considering distinct values of the nonlinearity r, we calculate several fractal dimensions characterizing percolation clusters. For the dimension associated with the red bonds we show that $d_{\scriptsize red} = 1/\nu$ at least to order {\sl O} (\epsilon^4), with $\nu$ being the correlation length exponent, and $\epsilon = 6-d$, where d denotes the spatial dimension. This result agrees with a rigorous one by Coniglio. Our result for the chemical distance, d_{\scriptsize min} = 2 - \epsilon /6 - [ 937/588 + 45/49 (\ln 2 -9/10 \ln 3)] (\epsilon /6)^2 + {\sl O} (\epsilon^3) verifies a previous calculation by one of us. For the backbone dimension we find D_B = 2 + \epsilon /21 - 172 \epsilon^2 /9261 + 2 (- 74639 + 22680 \zeta (3))\epsilon^3 /4084101 + {\sl O} (\epsilon^4), where $\zeta (3) = 1.202057...$, in agreement to second order in $\epsilon$ with a two-loop calculation by Harris and Lubensky.Comment: 29 pages, 7 figure