Phase Transition in a Self-repairing Random Network

TL;DR

This paper studies a self-repairing random network model where bonds are removed randomly but only if the network remains connected, revealing a phase transition at a critical bond concentration where the network's backbone disappears.

Contribution

It introduces a self-repairing bond percolation model and identifies a phase transition point where the network's backbone vanishes, relevant for porous materials and polymer degradation.

Findings

Phase transition at finite bond concentration p_c

Backbone of the network vanishes at p_c

Network remains dense and fractal below p_c

Abstract

We consider a network, bonds of which are being sequentially removed; that is done at random, but conditioned on the system remaining connected (Self-Repairing Bond Percolation SRBP). This model is the simplest representative of a class of random systems for which forming of isolated clusters is forbidden. It qualitatively describes the process of fabrication of artificial porous materials and degradation of strained polymers. We find a phase transition at a finite concentration of bonds $p=p_c$, at which the backbone of the system vanishes; for all $p<p_c$ the network is a dense fractal.