Localization transition, Lifschitz tails, and rare-region effects in network models

Géza Ódor
Phys. Rev. E 90, 032110 – Published 11 September 2014

Abstract

Effects of heterogeneity in the suspected-infected-susceptible model on networks are investigated using quenched mean-field theory. The emergence of localization is described by the distributions of the inverse participation ratio and compared with the rare-region effects appearing in simulations and in the Lifschitz tails. The latter, in the linear approximation, is related to the spectral density of the Laplacian matrix and to the time dependent order parameter. I show that these approximations indicate correctly Griffiths phases both on regular one-dimensional lattices and on small-world networks exhibiting purely topological disorder. I discuss the localization transition that occurs on scale-free networks at γ=3 degree exponent.

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  • Received 16 June 2014

DOI:https://doi.org/10.1103/PhysRevE.90.032110

©2014 American Physical Society

Authors & Affiliations

Géza Ódor

  • Research Center for Natural Sciences, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary

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Issue

Vol. 90, Iss. 3 — September 2014

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