Theory of continuum percolation II. Mean field theory

Abstract

I use a previously introduced mapping between the continuum percolation model and the Potts fluid to derive a mean field theory of continuum percolation systems. This is done by introducing a new variational principle, the basis of which has to be taken, for now, as heuristic. The critical exponents obtained are $\beta =1$, $\gamma =1$ and $\nu =0.5$, which are identical with the mean field exponents of lattice percolation. The critical density in this approximation is $ρ_c = 1/\ve$ where $\ve = \int d \x \, p(\x) \{ \exp [- v(\x)/kT] - 1 \}$. $p(\x)$ is the binding probability of two particles separated by $\x$ and $v(\x)$ is their interaction potential.

arXiv comment25 pages, Latex

References in corpus (1)

• Theory of continuum percolation I. General formalism

Cited by in corpus (4)

• Vogel-Fulcher freezing in relaxor ferroelectrics
• Equivalent-neighbor percolation models in two dimensions: crossover between mean-field and short-range behavior
• Exact solution of a one-dimensional continuum percolation model
• Dynamical Stability and Critical Exponents of the Neutral (S-type) Gubser-Rocha Model with Momentum Dissipation