Physics – Condensed Matter – Statistical Mechanics
Scientific paper
1999-10-26
Phys. Rev. E 61, 4821-4834 (2000)
Physics
Condensed Matter
Statistical Mechanics
29 pages, 7 figures
Scientific paper
10.1103/PhysRevE.61.4821
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.
Janssen Hans-Karl
Stenull Olaf
No associations
LandOfFree
Diluted Networks of Nonlinear Resistors and Fractal Dimensions of Percolation Clusters does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Diluted Networks of Nonlinear Resistors and Fractal Dimensions of Percolation Clusters, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Diluted Networks of Nonlinear Resistors and Fractal Dimensions of Percolation Clusters will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-24508