Phase Transition in a Self-repairing Random Network

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.

4 pages, 4 figures

References in corpus (4)

• Conductivity Exponent and Backbone Dimension in 2-d Percolation
• Minimum spanning trees on random networks
• Universality of finite-size corrections to the number of critical percolation clusters
• A quasi-random spanning tree model for the early river network

Cited by in corpus (5)

• Optimal Path and Minimal Spanning Trees in Random Weighted Networks
• Scale-Free Networks Emerging from Weighted Random Graphs
• Disorder Induced Limited Path Percolation
• "Burning and sticking" model for a porous material: suppression of the topological phase transition due to the backbone reinforcement effect
• Universality and non-universality in behavior of self-repairing random networks