## Abstract

The resistance of a random super-normal conductor network is calculated through the diffusion of a 'termite', which performs a random walk on the normal bonds and has the same probability to exist from any point on a cluster of superconducting bonds. The first time, T, that the termite exits at a distance r from the origin (averaged over many configurations and runs) is found to behave as T approximately r^{2}k/ for r<< xi ( xi is the percolation correlation length) and as T approximately r^{2}(p_{c}-p) ^{s} for r>> xi (( p_{c}-p)^{-s} describes the divergence of the conductivity as p to p_{c}^{-}, p being the concentration of the superconductor). Scaling arguments are used to show that k=1+s/(2+ theta ), where (2+ theta ) is the fractal dimension of random walks on single clusters at p_{c}. Numerical simulations at two dimensions (d=2) yields s=1.34+or-0.10 and k=1.34+or-0.03, in agreement with scaling. The authors also show that the probability of return to the origin at time t behaves as t^{-dk}2/. Preliminary results at d=1 and other calculations methods are also discussed.

Original language | English |
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Article number | 006 |

Pages (from-to) | L129-L136 |

Journal | Journal of Physics A: General Physics |

Volume | 18 |

Issue number | 3 |

DOIs | |

State | Published - 1 Dec 1985 |

Externally published | Yes |