Explosive site percolation and finite size hysteresis

TL;DR

This paper determines the critical point for explosive site percolation on 2D lattices using Monte Carlo simulations, revealing potential differences in universality class compared to bond percolation and analyzing finite size effects.

Contribution

It provides the first estimate of the explosive site percolation threshold and suggests it may belong to a different universality class than bond percolation.

Findings

Explosive site percolation threshold is approximately 0.695.

Evidence suggests different universality class from bond percolation.

Finite size effects cause differences between direct and reverse processes.

Abstract

We report the critical point for site percolation for the "explosive" type for 2D square lattices using Monte Carlo simulations and compare it to the classical well known percolation. We use similar algorithms as have been recently reported for bond percolation and networks. We calculate the "explosive" site percolation threshold as $p_c=0.695$ and we find evidence that "explosive" site percolation surprisingly may belong to a different universality class than bond percolation on lattices, providing that the transitions (a) are continuous and (b) obey the conventional finite size scaling forms. We do not attempt to determine the order of the explosive transition. Finally, we study and compare the direct and reverse processes, showing that while the reverse process is different from the direct process for finite size systems, the two cases become equivalent in the thermodynamic limit of large $L$.