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Critical behavior of the Ising and Blume-Capel models on directed two-dimensional small-world networks

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Abstract

The critical properties of the two-dimensional Ising and Blume-Capel model on directedsmall-world lattices with quenched connectivity disorder are investigated. The disordered system is simulated by applying the Monte Carlo method with heat bath update algorithm and histogram re-weighting techniques. The critical temperature, as well as the critical exponents are obtained. For both models the critical parameters have been obtained for several values of the rewiring probability p. It is found that these disorder systems do not belong to the same universality class as two-dimensional ferromagnetic model on regular lattices. In particular, the Blume-Capel model, with zero crystal field interaction, on a directedsmall-world lattice presents a second-order phase transition for p < p c , and a first-order phase transition for p > p c , where p c  ≈ 0.25. The critical exponents for p < p c are different from those of the same model on a regular lattice, but are identical to the exponents of the Ising model on directedsmall-world lattice.

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References

  1. R. Albert, A.-L. Barabási, Rev. Mod. Phys. 74, 47 (2002)

    Article  ADS  MATH  Google Scholar 

  2. D.J. Watts, S.W. Strogatz, Nature 393, 440 (1998)

    Article  ADS  Google Scholar 

  3. M.A. Novotny, Shannon M. Wheeler, Braz. J. Phys. 34, 395 (2004)

    Article  ADS  Google Scholar 

  4. D.P. Belanger, Braz. J. Phys. 30, 682 (2000)

    Article  ADS  Google Scholar 

  5. A. Barrat, M. Weigt, Eur. Phys. J. B 13, 547 (2000)

    Article  ADS  Google Scholar 

  6. M. Hinczewski, A.N. Berker, Phys. Rev. E 73, 066126 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  7. A.D. Sánchez, J.M. Lopes, M.A. Rodriguez, Phys. Rev. Lett. 88, 048701 (2002)

    Article  ADS  Google Scholar 

  8. F.W.S. Lima, E.M.S. Luz, R.N. Costa Filho, Multi-discip. Model. Mat. Str. 4, 1 (2009)

    Google Scholar 

  9. P.L. Ecuyer, Commun. ACM 31, 742 (1988)

    Article  Google Scholar 

  10. F.W.S. Lima, D. Stauffer, Physica A 359, 423 (2006)

    Article  ADS  Google Scholar 

  11. F.P. Fernandes, F.W.S. Lima, J.A. Plascak, Comput. Phys. Commun. 181, 1218 (2010)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. M.S.S. Challa, D.P. Landau, K. Binder, Phys. Rev. B 34, 1841 (1986)

    Article  ADS  Google Scholar 

  13. W. Janke, Phys. Rev. B 47, 14757 (1993)

    Article  ADS  Google Scholar 

  14. K. Binder, D.J. Herrmann, in Monte-Carlo Simulation in Statistical Physics, edited by P. Fulde (Springer-Verlag, Berlin, 1988), pp. 61–62

  15. W. Janke, R. Villanova, Phys. Lett. A 209, 179 (1995)

    Article  ADS  Google Scholar 

  16. P.E. Berche, C. Chatelain, B. Berche, Phys. Rev. Lett. 80, 297 (1998)

    Article  ADS  Google Scholar 

  17. K. Binder, Z. Phys. B 43, 119 (1981)

    Article  ADS  Google Scholar 

  18. X.S. Chen, V. Dohm, Phys. Rev. E 70, 056136 (2004)

    Article  ADS  Google Scholar 

  19. W. Selke, L.N. Shchur, J. Phys. A 38, L739 (2005)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. E. Brezin, J. Zinn-Justin, Nucl. Phys. B 257, 867 (1985)

    Article  ADS  Google Scholar 

  21. M.B. Hastings, Phys. Rev. Lett. 91, 098701 (2003)

    Article  ADS  Google Scholar 

  22. J.W. Duncan, Small Worlds: The Dynamics of Networks between Order and Randomness, in Princeton Studies in Complexity (Princeton University Press, 2004)

  23. J.-S. Wang, W. Selke, V I.S. Dotsenko, V.B. Andreichenko, Physica A 164, 221 (1990)

    Article  ADS  Google Scholar 

  24. P.H.L. Martins, J.A. Plascak, Phys. Rev. E 76, 012102 (2007)

    Article  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. Dietrich Stauffer Computational Physics Lab, Departamento de Física, Universidade Federal do Piauí, 64049-550, Teresina, PI, Brazil

    F.W.S. Lima & J.A. Plascak

  2. Departamento de Física, Universidade Federal de Minas Gerais, C.P. 702, 30123-970, Belo Horizonte, MG, Brazil

    J.A. Plascak

  3. Center for Simulational Physics, University of Georgia, 30602, Athens-GA, USA

    J.A. Plascak

  4. Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, OX1 3NP, Oxford, England

    J.A. Plascak

Authors
  1. F.W.S. Lima
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  2. J.A. Plascak
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Correspondence to J.A. Plascak.

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Lima, F., Plascak, J. Critical behavior of the Ising and Blume-Capel models on directed two-dimensional small-world networks. Eur. Phys. J. B 86, 300 (2013). https://doi.org/10.1140/epjb/e2013-40165-5

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