Abstract
We calculate the average resistanceR(L) of lattice animals spanningL×L cells on the square lattice using exact and Monte Carlo methods. The dynamical resistivity exponent, defined asR(L) ∼ L ζ, is found to be ζ=1.36±0.07. This contradicts the Alexander-Orbach conjecture, which predicts ζ≈ 0.8. Our value for ζ differs from earlier measurements of this quantity by other methods yielding ζ=1.17±0.05 and 1.22±0.08 by Havlin et al.
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On leave from the Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, China.
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Lam, P.M., Hansen, A. Resistivity exponent of two-dimensional lattice animals. J Stat Phys 52, 447–451 (1988). https://doi.org/10.1007/BF01016425
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DOI: https://doi.org/10.1007/BF01016425