Condensed Matter Physics, 2013, vol. 16, No. 2:115
DOI:10.5488/CMP.16.23602
arXiv:1302.3386
Title:
Phase transitions in the Potts model on complex networks
Author(s):

M. Krasnytska
(Institute for Condensed Matter Physics, NAS of Ukraine, 79011 Lviv, Ukraine;
Institut Jean Lamour, Universite de Lorraine, F54506 Vandoe uvre les Nancy, France)
,


B. Berche
(Institut Jean Lamour, Universite de Lorraine, F54506 Vandoe uvre les Nancy, France)


Yu. Holovatch
(Institute for Condensed Matter Physics, NAS of Ukraine, 79011 Lviv, Ukraine)

The Potts model is one of the most popular spin models of
statistical physics. The prevailing majority of work done so far
corresponds to the lattice version of the model. However, many
natural or manmade systems are much better described by the
topology of a network. We consider the qstate Potts model on an
uncorrelated scalefree network for which the nodedegree
distribution manifests a powerlaw decay governed by the exponent
\lambda. We work within the meanfield approximation, since for
systems on random uncorrelated scalefree networks this method is
known often to give asymptotically exact results. Depending on
particular values of q and \lambda one observes either a
firstorder or a secondorder phase transition or the system is
ordered at any finite temperature. In a case study, we consider the
limit q=1 (percolation) and find a correspondence between the
magnetic exponents and those describing percolation on a scalefree
network. Interestingly, logarithmic corrections to scaling appear at
\lambda=4 in this case.
Key words:
Potts model, complex networks, percolation, critical exponents
PACS:
64.60.ah, 64.60.aq, 64.60.Bd
