Discontinuous transition in an equilibrium percolation model with suppression

TL;DR

This paper demonstrates that an equilibrium percolation model with suppression exhibits a discontinuous transition at low initial seed concentrations, contrasting with previous non-equilibrium models, due to size-dependent growth suppression.

Contribution

It introduces a modified equilibrium percolation model with size-dependent suppression, revealing discontinuous transitions at low seed concentrations, unlike prior models.

Findings

Discontinuous transition occurs at low seed concentration rho.

Suppression of cluster growth leads to compact spanning clusters.

Transition behavior differs from non-equilibrium percolation models.

Abstract

Discontinuous transition is observed in the equilibrium cluster properties of a percolation model with suppressed cluster growth as the growth parameter g0 is tuned to the critical threshold at sufficiently low initial seed concentration rho in contrast to the previously reported results on non- equilibrium growth models. In the present model, the growth process follows all the criteria of the original percolation model except continuously updated occupation probability of the lattice sites that suppresses the growth of a cluster according to its size. As rho varied from higher values to smaller values, a line of continuous transition points encounters a coexistence region of spanning and non- spanning large clusters. At sufficiently small values of rho (less equal 0.05), the growth parameter g0 exceeds the usual percolation threshold and generates compact spanning clusters leading to discontinuous transitions.