Universality and non-universality in behavior of self-repairing random networks

Abstract

We numerically study one-parameter family of random single-cluster systems. A finite-concentration topological phase transition from the net-like to the tree-like phase (the latter is without a backbone) is present in all models of the class. Correlation radius index ${\nu }_B$ of the backbone in the net-like phase; graph dimensions -- $d_{\min }$ of the tree-like phase, and $D_{\min }$ of the backbone in the net-like phase appear to be universal within the accuracy of our calculations, while the backbone fractal dimension $D_B$ is not universal: it depends on the parameter of a model.

Published variant; more accurate numerical data and minor corrections. 4 pages, 5 figures

References in corpus (3)

• Conductivity Exponent and Backbone Dimension in 2-d Percolation
• A fast algorithm for backbones
• Phase Transition in a Self-repairing Random Network