• DOI:10.1103/PhysRevE.88.022140
• Corpus ID: 24046421

Continuum percolation of overlapping disks with a distribution of radii having a power-law tail.

@article{Sasidevan2013ContinuumPO,
  title={Continuum percolation of overlapping disks with a distribution of radii having a power-law tail.},
  author={V. Sasidevan},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2013},
  volume={88 2},
  pages={
          022140
        }
}

• V. Sasidevan
• Published 1 February 2013
• Physics
• Physical review. E, Statistical, nonlinear, and soft matter physics

We study the continuum percolation problem of overlapping disks with a distribution of radii having a power-law tail; the probability that a given disk has a radius between R and R+dR is proportional to R(-(a+1)), where a>2. We show that in the low-density nonpercolating phase, the two-point function shows a power-law decay with distance, even at arbitrarily low densities of the disks, unlike the exponential decay in the usual percolation problem. As in the problem of fluids with long-range interaction, we argue that in our problem, the critical exponents take their short-range values for a>3-η(sr) whereas they depend on a for a<3-η(sr) where η(sr) is the anomalous dimension for the usual percolation problem. The mean-field regime obtained in the fluid problem corresponds to the fully covered regime, a≤2, in the percolation problem. We propose an approximate renormalization scheme to determine the correlation length exponent ν and the percolation threshold. We carry out Monte Carlo simulations and determine the exponent ν as a function of a. The determined values of ν show that it is independent of the parameter a for a>3-η(sr) and is equal to that for the lattice percolation problem, whereas ν varies with a for 2