https://doi.org/10.1140/epjb/e2004-00019-y
Potts model on complex networks
1
Departamento de Física and Centro de Física do
Porto, Faculdade de Ciências, Universidade do Porto,
Rua do Campo Alegre 687, 4169-007 Porto, Portugal
2
A.F. Ioffe Physico-Technical Institute, 194021 St. Petersburg, Russia
3
Departamento de Física, Universidade
de Aveiro, Campus Universitário de Santiago, 3810-193 Aveiro, Portugal
Corresponding author: a jfmendes@fis.ua.pt
Received:
23
October
2003
Revised:
3
December
2003
Published online:
17
February
2004
We consider the general p-state Potts model on random networks with a given degree distribution (random Bethe lattices). We find the effect of the suppression of a first order phase transition in this model when the degree distribution of the network is fat-tailed, that is, in more precise terms, when the second moment of the distribution diverges. In this situation the transition is continuous and of infinite order, and size effect is anomalously strong. In particular, in the case of p=1, we arrive at the exact solution, which coincides with the known solution of the percolation problem on these networks.
PACS: 05.10.-a – Computational methods in statistical physics and nonlinear dynamics / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 05.50.+q – Lattice theory and statistics (Ising, Potts, etc.) / 87.18.Sn – Neural networks
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2004
