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Condensed Matter

arXiv:cond-mat/9606195 (cond-mat)
[Submitted on 26 Jun 1996]

Title:Theory of continuum percolation I. General formalism

Authors:Alon Drory
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Abstract: The theoretical basis of continuum percolation has changed greatly since its beginning as little more than an analogy with lattice systems. Nevertheless, there is yet no comprehensive theory of this field. A basis for such a theory is provided here with the introduction of the Potts fluid, a system of interacting $s$-state spins which are free to move in the continuum. In the $s \to 1$ limit, the Potts magnetization, susceptibility and correlation functions are directly related to the percolation probability, the mean cluster size and the pair-connectedness, respectively. Through the Hamiltonian formulation of the Potts fluid, the standard methods of statistical mechanics can therefore be used in the continuum percolation problem.
Comments: 26 pages, Latex
Subjects: Condensed Matter (cond-mat)
Cite as: arXiv:cond-mat/9606195
  (or arXiv:cond-mat/9606195v1 for this version)
  https://doi.org/10.48550/arXiv.cond-mat/9606195
Journal reference: Phys Rev E 54 (1996) 5992
Related DOI: https://doi.org/10.1103/PhysRevE.54.5992

Submission history

From: Alon Drory [view email]
[v1] Wed, 26 Jun 1996 09:13:20 UTC (15 KB)
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