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)

Effects of surfaces on resistor percolation

We study the effects of surfaces on resistor percolation at the instance of a semi-infinite geometry. Particularly we are interested in the average resistance between two connected ports located on the surface. Based on general grounds as symmetries and relevance we introduce a field theoretic Hamiltonian for semi-infinite random resistor networks. We show that the surface contributes to the average resistance only in terms of corrections to scaling. These corrections are governed by surface resistance exponents. We carry out renormalization group improved perturbation calculations for the special and the ordinary transition. We calculate the surface resistance exponents \phi_{\mathcal S \mathnormal} and \phi_{\mathcal S \mathnormal}^\infty for the special and the ordinary transition, respectively, to one-loop order.Comment: 19 pages, 3 figure

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

The Critical Behaviour of the Spin-3/2 Blume-Capel Model in Two Dimensions

The phase diagram of the spin-3/2 Blume-Capel model in two dimensions is explored by conventional finite-size scaling, conformal invariance and Monte Carlo simulations. The model in its $\tau$-continuum Hamiltonian version is also considered and compared with others spin-3/2 quantum chains. Our results indicate that differently from the standard spin-1 Blume-Capel model there is no multicritical point along the order-disorder transition line. This is in qualitative agreement with mean field prediction but in disagreement with previous approximate renormalization group calculations. We also presented new results for the spin-1 Blume-Capel model.Comment: latex 18 pages, 4 figure

Minifábricas: tecnologia social para processamento de castanha de caju.

O objetivo principal dessa sistematização é avaliar uma experiência de intervenção para o desenvolvimento local, gerando aprendizado para subsidiar futuras ações de TT, por meio de erros e acertos. Para tanto, buscou-se identificar e compreender os fatores que influenciaram a paralisação de 90% das minifábricas de castanha-de-caju, a partir de uma análise em três níveis: o papel da organização social; as relações de poder; e a gestão administrativa, econômica e financeira. Ao mesmo tempo, analisou-se o método de transferência de tecnologia e construção do conhecimento.bitstream/item/176503/1/OLV18001.pd

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