Abstract
A reanalysis of the resistanceR of two-and three-dimensional superconducting networks at the percolation thresholdp c , together with the previous results for the elastic moduliK of such networks, shows that there is aunified description of finite-size scaling for scalar and vector transport properties of percolation systems. For a network of linear sizeL atp c , and forboth scalar and vector percolation inboth two and three dimensions,K andR scale withL asL −x[a 1+a 2(lnL)−1+a 3 L −1], wherex is the ratio of the associated critical exponent ofK orR and the correlation length exponentv of percolation. Although our estimates ofx for the resistance of percolation networks are consistent with the previous results, they do indicate that inboth two and three dimensions and forboth scalar and vector percolation, the leading nonanalytic correction-to-scaling exponent iszero. From a reanalysis of data on diffusion on percolation clusters atp c , we propose that such correction-to-scaling terms are a general property ofdynamics of percolation clusters. We also suggest that for two-dimensional percolation the conductivity exponentt and the superconductivity exponents are given by s=t=v-{β}/4=187/144=1.2986..., and the elasticity exponentf is given byf=t+2v=571/144=3.9652..., whereβ is the exponent of the strength of the infinite percolation cluster.
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Sahimi, M., Arbabi, S. On correction to scaling for two- and three-dimensional scalar and vector percolation. J Stat Phys 62, 453–461 (1991). https://doi.org/10.1007/BF01020881
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DOI: https://doi.org/10.1007/BF01020881