Longest path in percolating hierarchical lattice |
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Authors: | P. Sen P. Ray |
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Affiliation: | (1) Saha Institute of Nuclear Physics, 700009 Calcutta, India;(2) Present address: Department of Physics, University of Manchester, M13 9PL, UK |
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Abstract: | We determine numerically the probability distribution for the longest self-avoiding path lengths connecting two distant points on a diluted hierarchical lattice at the percolation threshold. The evolution of this distribution with the system size is studied and the distribution is observed to approach a universal scale-invariant form under proper rescaling of its argument. The longest path length scales as |pmax| and our estimate for max=1.816±0.013 is clearly different from the previously estimated min=1.531+0.002 for the shortest path lengths on the same hierarchical lattice. This gives support to the multifractal behavior of SAWs on percolating clusters. |
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Keywords: | Self-avoiding walk percolation threshold critical exponents multifractal behavior |
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