q-state Potts model on the Apollonian network

Nuno A. M. Araújo, Roberto F. S. Andrade, and Hans J. Herrmann
Phys. Rev. E 82, 046109 – Published 18 October 2010

Abstract

The q-state Potts model is studied on the Apollonian network with Monte Carlo simulations and the transfer matrix method. The spontaneous magnetization, correlation length, entropy, and specific heat are analyzed as a function of temperature for different number of states, q. Different scaling functions in temperature and q are proposed. A quantitative agreement is found between results from both methods. No critical behavior is observed in the thermodynamic limit for any number of states.

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  • Received 26 July 2010

DOI:https://doi.org/10.1103/PhysRevE.82.046109

©2010 American Physical Society

Authors & Affiliations

Nuno A. M. Araújo1,*, Roberto F. S. Andrade2,†, and Hans J. Herrmann1,3,‡

  • 1Computational Physics for Engineering Materials, IfB, ETH Zurich, Schafmattstr. 6, 8093 Zurich, Switzerland
  • 2Instituto de Física, Universidade Federal da Bahia, 40210-210 Salvador, BA, Brazil
  • 3Departamento de Física, Universidade Federal do Ceará, Campus do Pici, 60451-970 Fortaleza, CE, Brazil

  • *nuno@ethz.ch
  • randrade@ufba.br
  • hans@ifb.baug.ethz.ch

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Issue

Vol. 82, Iss. 4 — October 2010

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