Trading interactions for topology in scale-free networks.
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)proportional to(q(i)q(j))(-mu). 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.
Giuraniuc
C V
CV
Laboratorium voor Vaste-Stoffysica en Magnetisme, Katholieke Universiteit Leuven, 3001 Leuven, Belgium.
Hatchett
J P L
JP
Indekeu
J O
JO
Leone
M
M
Pérez Castillo
I
I
Van Schaeybroeck
B
B
Vanderzande
C
C