Ising models on the Regularized Apollonian Network

Abstract

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.

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• Ising model on the Apollonian network with node dependent interactions
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• q-state Potts model on the Apollonian network
• Nonequilibrium Zaklan model on Apollonian Networks
• Exact and Approximate Solutions for the Dilute Ising Model
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Cited by in corpus (5)

• Generalized open quantum walks on Apollonian networks
• Ising Model on a random network with annealed or quenched disorder
• Exact evaluation of the causal spectrum and localization properties of electronic states on a scale-free network
• Exactly solvable tight-binding model on the RAN: fractal energy spectrum and Bose-Einstein condensation
• Exact critical-temperature bounds for two-dimensional Ising models