q-state Potts model on the Apollonian network

Nuno A. M. Araújo, Roberto F. S. Andrade, Hans J. Herrmann

Published 2010-07-26, updated 2010-10-18Version 2

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.