  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.
