title: q-state Potts model on the Apollonian network.
abstract: The q-state Potts model is studied on the Apollonian network with Monte Carlo simulations and the transfer matrix method. The spontaneous magnetization, correlation length, entropy, and specific heat are analyzed as a function of temperature for different number of states, q. Different scaling functions in temperature and q are proposed. A quantitative agreement is found between results from both methods. No critical behavior is observed in the thermodynamic limit for any number of states.
authors.affiliation: Computational Physics for Engineering Materials, IfB, ETH Zurich, Schafmattstr 6, 8093 Zurich, Switzerland. nuno@ethz.ch
authors.forename: Nuno A M
authors.initials: NA
authors.lastname: Araújo
authors.forename: Roberto F S
authors.initials: RF
authors.lastname: Andrade
authors.forename: Hans J
authors.initials: HJ
authors.lastname: Herrmann