Ising models on the regularized Apollonian network.
We investigate the critical properties of Ising models on a regularized Apollonian network (RAN), here defined as a kind of Apollonian network in which the connectivity asymmetry associated with 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 behavior. While ordinary ferromagnetic and antiferromagnetic models on a RAN do not undergo a phase transition, some antiferrimagnetic 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 an intermediate step for the calculation of the partition function and the order parameters.
Departamento de Biofísica e Farmacologia, Universidade Federal do Rio Grande do Norte, 59072-970 Natal, Rio Grande do Norte, Brazil and Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica, Università dell'Aquila, 67010 L'Aquila, Italy.
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Albuquerque