The Resistance of Feynman Diagrams and the Percolation Backbone Dimension

Details The Resistance of Feynman Diagrams and the Percolation Backbone Dimension The Resistance of Feynman Diagrams and the Percolation Backbone Dimension

1999-01-21

arxiv.org/abs/cond-mat/9901223v1

Phys. Rev. E 59, R6239-R6242 (1999)

Physics

Condensed Matter

Statistical Mechanics

10 pages, 2 figures

Scientific paper

10.1103/PhysRevE.59.R6239

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 $\zeta (3) = 1.202057..$.

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