Conduction and connection properties of self-avoiding walks with bridges

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Abstract
The voltage drop distribution in the random-resistor networks constituted by all nearest-neighbor bonds connecting points visited by a lattice self-avoiding walk (SAW) is studied by accurate numerical techniques in d=2. An analysis of the moments of the distribution allows one to establish the value ζ=1.333±0.007 for the resistance exponent and to exclude the possibility of multifractal behavior. These results are also consistent with a topological investigation of the connection properties of SAW, which independently yields ζ=1.33±0.01. This clearly supports ζ=(4/3 and a spectral dimension d̃=1 for these walks, solving an old controversy. A possible extension of such an analysis to SAW at the FTHETA point is also discussed.

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