Criticality on networks with topology-dependent interactions

C. V. Giuraniuc*, J. P.L. Hatchett, J. O. Indekeu, M. Leone, I. Pérez Castillo, B. Van Schaeybroeck, C. Vanderzande

*Corresponding author for this work

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

Weighted scale-free networks with topology-dependent interactions are studied. It is shown that the possible universality classes of critical behavior, which are known to depend on topology, can also be explored by tuning the form of the interactions at fixed topology. For a model of opinion formation, simple mean field and scaling arguments show that a mapping Y' (Y-μ)/(1-μ) describes how a shift of the standard exponent Y of the degree distribution can absorb the effect of degree-dependent pair interactions Jij (ki kj)μ, where ki stands for the degree of vertex i. This prediction is verified by extensive numerical investigations using the cavity method and Monte Carlo simulations. The critical temperature of the model is obtained through the Bethe-Peierls approximation and with the replica technique. The mapping can be extended to nonequilibrium models such as those describing the spreading of a disease on a network.

Original languageEnglish
Article number036108
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume74
Issue number3
DOIs
Publication statusPublished - 1 Jan 2006

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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    Giuraniuc, C. V., Hatchett, J. P. L., Indekeu, J. O., Leone, M., Pérez Castillo, I., Van Schaeybroeck, B., & Vanderzande, C. (2006). Criticality on networks with topology-dependent interactions. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 74(3), [036108]. https://doi.org/10.1103/PhysRevE.74.036108