Transport on exploding percolation clusters

TL;DR

This paper introduces a generalized explosive percolation model where the selection process influences the structural and transport properties, revealing that intermediate parameters lead to the poorest conductivity due to loop suppression.

Contribution

It presents a novel percolation process with a parameter q, showing how it affects critical exponents and transport properties, especially the conductivity.

Findings

Critical exponents vary continuously with q.

Intermediate q values result in minimal conductance.

Loop suppression explains reduced conductivity at intermediate q.

Abstract

We propose a simple generalization of the explosive percolation process [Achlioptas et al., Science 323, 1453 (2009)], and investigate its structural and transport properties. In this model, at each step, a set of q unoccupied bonds is randomly chosen. Each of these bonds is then associated with a weight given by the product of the cluster sizes that they would potentially connect, and only that bond among the q-set which has the smallest weight becomes occupied. Our results indicate that, at criticality, all finite-size scaling exponents for the spanning cluster, the conducting backbone, the cutting bonds, and the global conductance of the system, change continuously and significantly with q. Surprisingly, we also observe that systems with intermediate values of q display the worst conductive performance. This is explained by the strong inhibition of loops in the spanning cluster, resulting in a substantially smaller associated conducting backbone.