Self-avoiding walks on random networks of resistors and diodes

D. Marković, S. Milošević and H.E. Stanley

Physica A: Statistical Mechanics and its Applications, 1987, vol. 144, issue 1, 1-16

Abstract: We study the self-avoiding walks (SAW) on a square lattice whose various degrees of randomness encompasses many different random networks, including the incipient clusters of the directed, mixed and isotropic bond percolation. We apply the position-space renormalization group (PSRG) method and demonstrate that within the framework of this method one is bound to find that the critical exponent v of the mean end-to-end distance of SAW on various two-dimensional random networks should be equal to the critical exponent of SAW on the ordinary square lattice. A detailed analysis of this finding, and similar findings of other authors, lead us to conclude that a debatable opposite finding, which has been predicted on the basis of different approaches, could be attained after a substantial refinement of the method applied.

Date: 1987
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:144:y:1987:i:1:p:1-16

DOI: 10.1016/0378-4371(87)90142-7

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