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.

[1]  S. N. Dorogovtsev,et al.  Critical phenomena in networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Katarzyna Sznajd-Weron,et al.  Opinion evolution in closed community , 2000, cond-mat/0101130.

[3]  A. Barabasi,et al.  Halting viruses in scale-free networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Sergey N. Dorogovtsev,et al.  Evolution of Networks: From Biological Nets to the Internet and WWW (Physics) , 2003 .

[5]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[6]  Deok-Sun Lee,et al.  Cascading toppling dynamics on scale-free networks , 2005 .

[7]  G. Bianconi.  Mean field solution of the Ising model on a Barabási–Albert network , 2002, cond-mat/0204455.

[8]  Sergey N. Dorogovtsev,et al.  Ising Model on Networks with an Arbitrary Distribution of Connections , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  A. Maritan,et al.  Derivation of Landau theories and lattice mean-field theories for surface and wetting phenomena, from semi-infinite Ising models , 1991 .

[10]  R. Zecchina,et al.  Ferromagnetic ordering in graphs with arbitrary degree distribution , 2002, cond-mat/0203416.

[11]  S. Galam,et al.  Sociophysics: A new approach of sociological collective behaviour. I. mean‐behaviour description of a strike , 1982, 2211.07041.

[12]  D. Stauffer,et al.  Ferromagnetic phase transition in Barabási–Albert networks , 2001, cond-mat/0112312.

[13]  F. Iglói,et al.  First- and second-order phase transitions in scale-free networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[15]  S. Strogatz.  Exploring complex networks , 2001, Nature.

[16]  Alessandro Vespignani,et al.  Epidemic dynamics and endemic states in complex networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  J. Indekeu.  Special attention network , 2003, physics/0310113.