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Ising models on the regularized Apollonian network.

M Serva1, U L Fulco, E L Albuquerque

  • 1Departamento 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.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 16, 2013
PubMed
Summary
This summary is machine-generated.

We studied Ising models on a regularized Apollonian network (RAN). Some antiferrimagnetic models on RANs exhibit an infinite-order phase transition, unlike ferromagnetic and antiferromagnetic models.

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Area of Science:

  • Statistical Mechanics
  • Complex Networks
  • Condensed Matter Physics

Background:

  • Ising models are fundamental for understanding magnetism and phase transitions.
  • Apollonian networks possess unique fractal properties and varying connectivity.
  • Regularized Apollonian networks (RANs) address connectivity asymmetry in standard Apollonian networks.

Purpose of the Study:

  • To investigate the critical properties of Ising models on a regularized Apollonian network (RAN).
  • To explore the impact of different coupling constants on phase transitions within RANs.
  • To identify conditions leading to phase transitions in these specific network structures.

Main Methods:

  • Exact analytical approach using iterative partial tracing.
  • Calculation of the partition function and order parameters.
  • Analysis of ferromagnetic, antiferromagnetic, and antiferrimagnetic models.

Main Results:

  • Ferromagnetic and antiferromagnetic Ising models on RANs do not exhibit a phase transition.
  • Certain antiferrimagnetic models on RANs display an infinite-order phase transition.
  • The study systematically analyzes critical behavior based on network topology and coupling configurations.

Conclusions:

  • The specific topology of RANs, combined with antiferrimagnetic interactions, can induce novel phase transitions.
  • Standard ferromagnetic and antiferromagnetic interactions are insufficient to drive phase transitions on RANs.
  • The analytical method provides a rigorous framework for studying critical phenomena on complex networks.