Grassmann Path Integral Approach to Two-Dimensional Percolation Near the Critical Point

  • Giancarlo Jug


The concept of percolation is a fundamental one in the physics of disordered systems and has been discussed at length at this Institute. Over the last decade, a consistent theory of percolation has emerged, borrowing heavily from the familiar description of critical phenomena. In particular, in two dimensions (2D) a small set of plausible assumptions has led to a conjectured exact theory for the asymptotic behaviour near the percolation threshold, pc.[1] Central amongst these is the assumption that the critical singularities are in the form of power laws.


Ising Model Percolation Threshold Critical Phenomenon Critical Line Critical Singularity 
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  1. 1.
    B.Nienhuis, J.Stat.Phys. 34, 731 (1984), and references thereinGoogle Scholar
  2. 2.
    G.Jug, Phys.Rev.Lett. 53, 9 (1984)Google Scholar
  3. 3.
    G.Jug, Phys.Rev.Lett. (submitted)Google Scholar
  4. 4.
    M.F.Sykes, private communicationGoogle Scholar
  5. 5.
    See also D.Andelman and A.N.Berker, J.Phys.A 14, L91 (1981)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Giancarlo Jug
    • 1
  1. 1.Process Physics DivisionAFRC-Food Research InstituteNorwichEngland

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