Crossover behavior of conductivity in a discontinuous percolation model
arXiv:1401.3924 · doi:10.1103/PhysRevE.89.032113
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.
References in corpus (10)
- Self-organized adaptation of a simple neural circuit enables complex robot behaviour
- Impact of Single Links in Competitive Percolation -- How complex networks grow under competition
- Explosive percolation via control of the largest cluster
- Avoiding a Spanning Cluster in Percolation Models
- Strongly discontinuous explosive percolation with multiple giant components
- Tricritical point in explosive percolation
- Watersheds are Schramm-Loewner Evolution curves
- Suppression effect on explosive percolations
- Bohman-Frieze-Wormald model on the lattice, yielding a discontinuous percolation transition
- Conductivity of Coniglio-Klein clusters