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

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

2009-03-12

arxiv.org/abs/0903.2089v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

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

Scientific paper

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.

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