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, , describes how a shift of the standard exponent of the degree distribution can absorb the effect of degree-dependent pair interactions . The 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 nonequilibrium systems, and is illustrated with interdisciplinary applications.
- Received 19 August 2004
DOI:https://doi.org/10.1103/PhysRevLett.95.098701
©2005 American Physical Society