First-order transition in a percolation model with nucleation and preferential growth.

Abstract

The spanning cluster properties of a percolation model with nucleation and preferential growth exhibit first-order transitions depending on the values of the growth parameter g_{0} and the initial seed concentration ρ. Except for the preferential growth of smaller clusters with a size-dependent growth probability of amplitude g_{0}, the model preserves all other criteria of the original percolation model. As ρ decreases starting from the percolation threshold p_{c} of the original percolation, a line of continuous transition encounters a coexistence region of percolative and nonpercolative large clusters. At sufficiently small values of ρ (≤0.05), the value of g_{0} exceeds p_{c} and generates compact spanning clusters leading to first-order discontinuous transitions.