title: Crossover behavior of conductivity in a discontinuous percolation model.
abstract: When conducting bonds are occupied randomly in a two-dimensional square lattice, the conductivity of the system increases continuously as the density of those conducting bonds exceeds the percolation threshold. Such a behavior is well known in percolation theory; however, the conductivity behavior has not been studied yet when the percolation transition is discontinuous. Here we investigate the conductivity behavior through a discontinuous percolation model evolving under a suppressive external bias. Using effective medium theory, we analytically calculate the conductivity behavior as a function of the density of conducting bonds. The conductivity function exhibits a crossover behavior from a drastically to a smoothly increasing function beyond the percolation threshold in the thermodynamic limit. The analytic expression fits well our simulation data.
authors.affiliation: Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Korea.
authors.forename: Seongmin
authors.initials: S
authors.lastname: Kim
authors.affiliation: Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Korea.
authors.forename: Y S
authors.initials: YS
authors.lastname: Cho
authors.affiliation: Computational Physics for Engineering Materials, IfB, ETH Zurich, Wolfgang-Pauli-Strasse 27, CH-8093 Zurich, Switzerland.
authors.forename: N A M
authors.initials: NA
authors.lastname: Araújo
authors.affiliation: Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Korea.
authors.forename: B
authors.initials: B
authors.lastname: Kahng