Criticality on networks with topology-dependent interactions

Details Criticality on networks with topology-dependent interactions Criticality on networks with topology-dependent interactions

2006-03-25

arxiv.org/abs/cond-mat/0603689v3

Physical Review E 74, 036108 (2006)

Physics

Condensed Matter

Statistical Mechanics

20 pages, 14 figures

Scientific paper

10.1103/PhysRevE.74.036108

Weighted 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 $\gamma'=(\gamma-\mu)/(1-\mu)$ describes how a shift of the standard exponent $\gamma$ of the degree distribution can absorb the effect of degree-dependent pair interactions $J_{ij} \propto (k_ik_j)^{-\mu}$, 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.

Affiliated with

Also associated with

No associations

Rating

Criticality on networks with topology-dependent interactions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Criticality on networks with topology-dependent interactions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Criticality on networks with topology-dependent interactions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-607849