Trading interactions for topology in scale-free networks

Details Trading interactions for topology in scale-free networks Trading interactions for topology in scale-free networks

2004-08-18

arxiv.org/abs/cond-mat/0408399v2

Physical Review Letters 95, 098701 (2005) (4pages),

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 5 figures

Scientific paper

10.1103/PhysRevLett.95.098701

Scale-free networks with topology-dependent interactions are studied. It is shown that the universality classes of critical behavior, which conventionally depend only on topology, can also be explored by tuning the interactions. A mapping, $\gamma' = (\gamma - \mu)/(1-\mu)$, describes how a shift of the standard exponent $\gamma$ of the degree distribution $P(q)$ can absorb the effect of degree-dependent pair interactions $J_{ij} \propto (q_iq_j)^{-\mu}$. Replica technique, cavity method and Monte Carlo simulation support the physical picture suggested by Landau theory for the critical exponents and by the Bethe-Peierls approximation for the critical temperature. The equivalence of topology and interaction holds for equilibrium and non-equilibrium systems, and is illustrated with interdisciplinary applications.

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