Dasgupta, C. ; Harris, A. B. ; Lubensky, T. C.
(1978)
*Renormalization-group treatment of the random resistor network in 6-ε dimensions
*
Physical Review B: Condensed Matter and Materials Physics, 17
(3).
pp. 1375-1382.
ISSN 1098-0121

Full text not available from this repository.

Official URL: http://prb.aps.org/abstract/PRB/v17/i3/p1375_1

Related URL: http://dx.doi.org/10.1103/PhysRevB.17.1375

## Abstract

We consider a hypercubic lattice in which neighboring points are connected by resistances which assume independently the random values σ_{>}^{-1} and σ_{<}^{-1 }with respective probabilities p and 1-p. For σ_{<}=0 the lattice is viewed as consisting of irreducible nodes connected by chains of path length L. This geometrical length is distinct from the characteristic length L_{r} which sets a scale of resistance in the random network or L_{m} which sets a scale of effective exchange in a dilute magnet. Near the percolation concentration p_{c} one sets L~|p-p_{c}|^{-ζ}, L_{r}~|p-p_{c}|-^{ζr} and L_{m}~|p-p_{c}|^{-ζm}. Stephen and Grest (SG) have already shown that ζ_{m}=1+o(ε^{2}) for spatial dimensionality d=6-ε. Here we show in a way similar to SG that ζ_{r}=1+o(ε^{2}). Thus it is possible that ζ_{m}=ζ_{r}=1 for a continuous range of d below 6. However, increasing evidence suggests that this equality does not hold for d<4, and in particular a calculation in 1+ε dimensions analogous to that of SG for ζ_{m} does not seem possible.

Item Type: | Article |
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Source: | Copyright of this article belongs to The American Physical Society. |

ID Code: | 83435 |

Deposited On: | 20 Feb 2012 12:09 |

Last Modified: | 20 Feb 2012 12:09 |

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