On the relationship between the critical exponents of percolation conductivity and static exponents of percolation

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Abstract
The author argues that the critical exponent t of random conductance networks near the percolation threshold is given by t=(d-1) nu for low dimensionalities and t=1+ beta ' for high dimensionalities, where nu is the correlation length exponent, beta ' the backbone exponent and d is dimensionality. The author argues that what separates the two regimes is a critical fractal dimensionality Dl which equals 2. The author also argues that Dl is also a critical fractal dimensionality for fractals such as lattice animals and diffusion-limited aggregates. The result for low dimensionalities has been also obtained by Aharony and Stauffer by a different argument.