Bond-site duality and phase transition nature of explosive percolations on a two-dimensional lattice

TL;DR

This paper investigates the duality and phase transition types of explosive percolation models on a 2D lattice, revealing a bond-site duality and contrasting discontinuous and continuous transitions based on intra-bond occupation.

Contribution

It establishes the bond-site duality for explosive percolation on a square lattice and characterizes the nature of phase transitions in different model variants.

Findings

Discontinuous transition in intra-bond-enhanced models with bond-site duality.

Continuous transition in intra-bond-suppressed models without duality.

Normal scaling behavior observed in intra-bond-suppressed models.

Abstract

To establish the bond-site duality of explosive percolations in 2 dimension, the site and bond explosive percolation models are carefully defined on a square lattice. By studying the cluster distribution function and the behavior of the second largest cluster, it is shown that the duality in which the transition is discontinuous exists for the pairs of the site model and the corresponding bond model which relatively enhances the intra-bond occupation. In contrast the intra-bond-suppressed models which have no corresponding site models undergo the continuous transition and satisfy the normal scaling ansatz as ordinary percolation.