Ising models on the Regularized Apollonian Network

TL;DR

This paper studies the critical behavior of Ising models on a Regularized Apollonian Network, revealing that ferromagnetic and anti-ferromagnetic models do not have phase transitions, but some anti-ferrimagnetic models exhibit infinite order transitions, using exact analytical methods.

Contribution

It introduces an exact analytical approach to analyze Ising models on the Regularized Apollonian Network, highlighting unique phase transition behaviors.

Findings

Ferromagnetic and anti-ferromagnetic models do not undergo phase transitions.

Some anti-ferrimagnetic models show infinite order transitions.

The approach uses iterative partial tracing of the Boltzmann factor.

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.