  We investigate the critical properties of Ising models on a Regularized
Apollonian Network (RAN), here defined as a kind of Apollonian Network (AN) in
which the connectivity asymmetry associated to its corners is removed.
Different choices for the coupling constants between nearest neighbors are
considered, and two different order parameters are used to detect the critical
behaviour. While ordinary ferromagnetic and anti-ferromagnetic models on RAN do
not undergo a phase transition, some anti-ferrimagnetic models show an
interesting infinite order transition. All results are obtained by an exact
analytical approach based on iterative partial tracing of the Boltzmann factor
as intermediate steps for the calculation of the partition function and the
order parameters.
