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 $\rho$. 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 $\rho$ 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 $\rho$ ($\le 0.05$), the value of $g_0$ exceeds $p_c$ and generates compact spanning clusters leading to first-order discontinuous transitions.