# The Resistance of Feynman Diagrams and the Percolation Backbone Dimension

Source: [The Resistance of Feynman Diagrams and the Percolation Backbone Dimension](<https://www.sota2.com/research/paper/68fa34261e209131ce896315>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-27T03:42:48.811Z

Authors: H. K. Janssen, O. Stenull, K. Oerding

Published: 1999-01-21T16:38:21.000Z

## Abstract

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

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/9901223>)

[PDF](<https://arxiv.org/pdf/cond-mat/9901223.pdf>)