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Trading interactions for topology in scale-free networks

C. V. Giuraniuc·J. P. L. Hatchett·J. O. Indekeu·M. Leone·I. Perez Castillo·B. Van Schaeybroeck·C. Vanderzande
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Abstract

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, $γ' = (γ- μ)/(1-μ)$, describes how a shift of the standard exponent $γ$ of the degree distribution $P(q)$ can absorb the effect of degree-dependent pair interactions $J_{ij} \propto (q_iq_j)^{-μ}$. 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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C. V. Giuraniuc, J. P. L. Hatchett, J. O. Indekeu, M. Leone, I. Perez Castillo, B. Van Schaeybroeck, C. Vanderzande. 2005-09-30. Trading interactions for topology in scale-free networks. https://doi.org/10.1103/physrevlett.95.098701

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