• Record: found
  • Abstract: found
  • Article: found
Is Open Access

Critical Percolation and Transport in Nearly One Dimension


Read this article at

      There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.


      A random hopping on a fractal network with dimension slightly above one, \(d = 1 + \epsilon\), is considered as a model of transport for conducting polymers with nonmetallic conductivity. Within the real space renormalization group method of Migdal and Kadanoff, the critical behavior near the percolation threshold is studied. In contrast to a conventional regular expansion in \(\epsilon\), the critical indices of correlation length, \(\nu =\epsilon ^{-1}+O(e^{-1/\epsilon })\), and of conductivity, \(t\simeq \epsilon^{-2} exp (-1-1/\epsilon )\), are found to be nonanalytic functions of \(\epsilon\) as \(\epsilon \to 0\). Distribution for conductivity of the critical cluster is obtained to be gaussian with the relative width \(\sim \exp (-1/\epsilon )\). In case of variable range hopping an ``1-d Mott's law'' \(exp [ -( T_t/T)^{1/2}]\) dependence was found for the DC conductivity. It is shown, that the same type of strong temperature dependence is valid for the dielectric constant and the frequency-dependent conductivity, in agreement with experimental data for poorly conducting polymers.

      Related collections

      Author and article information

      23 December 1996
      Custom metadata
      5 pages, RevTeX, 2 EPS figures included, to be published in Phys.Rev.Lett
      cond-mat.dis-nn cond-mat.stat-mech


      Comment on this article