Criticality on networks with topology-dependent interactions

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dc.creatorGiuraniuc, C. V.
dc.creatorHatchett, J. P. L.
dc.creatorIndekeu, J. O.
dc.creatorLeone, M.
dc.creatorCastillo, I. Perez
dc.creatorVan Schaeybroeck, B.
dc.creatorVanderzande, C.
dc.date2006-03-25
dc.date2006-09-22
dc.date.accessioned2026-07-07T07:04:58Z
dc.date.available2026-07-07T07:04:58Z
dc.descriptionWeighted scale-free networks with topology-dependent interactions are studied. It is shown that the possible universality classes of critical behaviour, 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 $γ'=(γ-μ)/(1-μ)$ describes how a shift of the standard exponent $γ$ of the degree distribution can absorb the effect of degree-dependent pair interactions $J_{ij} \propto (k_ik_j)^{-μ}$, where $k_i$ 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.
dc.description20 pages, 14 figures
dc.identifierhttps://arxiv.org/abs/cond-mat/0603689
dc.identifierhttp://arxiv.org/abs/cond-mat/0603689
dc.identifierPhysical Review E 74, 036108 (2006)
dc.identifierdoi:10.1103/PhysRevE.74.036108
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/109516
dc.subjectStatistical Mechanics
dc.subjectDisordered Systems and Neural Networks
dc.titleCriticality on networks with topology-dependent interactions
dc.typetext

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