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Journal of Statistical Physics

, Volume 35, Issue 1–2, pp 119–130 | Cite as

Tunneling resistivity of a one-dimensional random lattice and the petersburg problem

  • P. Palffy-Muhoray
  • R. Barrie
  • B. Bergersen
  • I. Carvalho
  • M. Freeman
Articles

Abstract

The resistivity of a one-dimensional lattice consisting of randomly distributed conducting and insulating sites is considered. Tunneling resistance of the form ρ0ne bn is assumed for a cluster ofn adjacent insulating sites. In the thermodynamic limit, the mean resistance per site diverges at the critical filling fractionp c =e−b, while the mean square resistivity fluctuations diverge at the lower filling fraction\(p_{c_2 } \)=p c 2 . Computer simulations of large but finite systems, however, show only a very weak divergence of resistivity atp c and no divergence of the fluctuations at\(p_{c_2 } \). For finite lattices, calculation of the resistivity at the critical filling is shown to be simply related to the Petersburg problem. Analytic expressions for the resistivity and resistivity fluctuations are obtained in agreement with the results of computer simulations.

Key words

Tunneling resistivity Petersburg problem random lattice fluctuations critical filling mean and most probable values divergence 

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Copyright information

© Plenum Publishing Corporation 1984

Authors and Affiliations

  • P. Palffy-Muhoray
    • 1
    • 2
  • R. Barrie
    • 1
  • B. Bergersen
    • 1
  • I. Carvalho
    • 1
  • M. Freeman
    • 1
    • 2
  1. 1.Department of PhysicsUniversity of British ColumbiaVancouverCanada
  2. 2.Department of PhysicsCapilano CollegeNorth VancouverCanada

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