Position space renormalisation group study of shortest paths in percolation clusters
- 1 August 1985
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 18 (11) , L657-L660
- https://doi.org/10.1088/0305-4470/18/11/005
Abstract
The average length of the shortest paths along the backbone of the incipient infinite cluster is expected to diverge near the percolation threshold pc as mod p-pc mod - nu s, with nu s different from the correlation length exponent nu . The author applies the position space renormalisation group (PSRG) technique to obtain nu s both for square and cubic lattices and for a triangular lattice in two dimensions. The results obtained ( nu s=1.49 for d=2 and 1.21 for d=3) are in very good agreement with the existing results obtained by different methods.Keywords
This publication has 8 references indexed in Scilit:
- Backbone and elastic backbone of percolation clusters obtained by the new method of 'burning'Journal of Physics A: General Physics, 1984
- Cumulant renormalisation group and its application to the incipient infinite cluster in percolationJournal of Physics A: General Physics, 1983
- Exact enumeration approach to fractal properties of the percolation backbone and 1/σ expansionJournal of Physics A: General Physics, 1983
- Correlation-length exponent in two-dimensional percolation and Potts modelPhysical Review B, 1981
- Large-cell Monte Carlo renormalization group for percolationPhysical Review B, 1980
- A relation between the temperature exponents of the eight-vertex and q-state Potts modelJournal of Physics A: General Physics, 1979
- Critical properties of site- and bond-diluted Ising ferromagnetsJournal of Physics C: Solid State Physics, 1979
- Real-space renormalization of bond-disordered conductance latticesPhysical Review B, 1978