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Upper Bounds on the Critical Temperature of the Ashkin-Teller Model

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Abstract

Starting from correlation identities for the Ashkin-Teller model and using correlation inequalities, we obtain rigorous upper bounds on the critical temperatures. The results were obtained in hexagonal, square, and cubic lattices and improve over effective field type calculations. The rigorous upper bounds results are compared to those obtained by other methods.

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References

  1. J. Ashkin, E. Teller, Phys. Rev. 64, 178 (1943)

    Article  ADS  Google Scholar 

  2. J.P. Santos, F.C. Sá Barreto, Physica A. 421, 316 (2015)

    Article  ADS  Google Scholar 

  3. R.V. Ditzian, R.J. Banavar, G.S. Grest, L.P. Kadanoff, Phys. Rev. B. 22, 2542 (1980)

    Article  MathSciNet  ADS  Google Scholar 

  4. P.L. Cristiano, S. Goulart Rosa Jr., Phys. Lett. 110A, 44 (1985)

    Article  ADS  Google Scholar 

  5. P.L. Cristiano, S. Goulart Rosa Jr., Phys. Rev. B. 33, 07 (1986)

    Google Scholar 

  6. J.A. Plascak, F.C. Sá Barreto, Physica A. 19, 2195 (1986)

    Google Scholar 

  7. P.M.C. Oliveira, F.C. Sá Barreto, J. Stat. Phys. 57, 53 (1989)

    Article  ADS  Google Scholar 

  8. P. Pawlicki, G. Musial, G. Kamieniarz, J. Rogiers, Physica A. 242, 281 (1997)

    Article  ADS  Google Scholar 

  9. N. Benayad, A. Benyoussef, N. Boccara, A. El. Kenz, J. Phys. C. 21, 5747 (1988)

    Article  ADS  Google Scholar 

  10. G. Kamieniarz, P. Kozlowski, R. Dekeyser. arXiv:cond-mat/9803277v1 (1998)

  11. P. Arnold, Y. Zhang, Nucl. Phys. B. 501, 803 (1997)

    Article  ADS  Google Scholar 

  12. D. Jeziorek-Kniola, G. Musial, L. Debski, J. Rogiers, S. Dylak, Acta Phys. Polo. A. 1105, 121 (2012)

    Google Scholar 

  13. G. Musial, L. Debski, G. Kamieniarz, Phys. Rev. B. 66, 012407 (2002)

    Article  ADS  Google Scholar 

  14. G. Musial, Phys. Status Solidi B. 236, 486 (2003)

    Article  ADS  Google Scholar 

  15. G. Musial, Phys. Rev. B. 69, 024407 (2004)

    Article  ADS  Google Scholar 

  16. G. Musial, J. Rogiers, Phys. Status Solidi B. 243, 335 (2006)

    Article  ADS  Google Scholar 

  17. P. Pawlicki, G. Musial, G. Kamieniarz, J. Rogiers, Physica A. 242, 281 (1997)

    Article  ADS  Google Scholar 

  18. M. Sluiter, Y. Kawazoe, Sci. Rep. RITU A. 40, 301 (1995)

    Google Scholar 

  19. M.S. Gronsleth, T.B. Nilssen, E.K. Dahl, E.B. Stiansen, C.M. Varma, A. Sudbo. arXiv:Cond-Mat/0806.2665v2 (2009)

  20. C. Zhe, W. Ping, Z. Ying-Hong, Commun. Theor. Phys. 49, 525 (2008)

    Article  ADS  Google Scholar 

  21. P. Bak, P. Kleban, W.N. Unertl, J. Ochab, G. Akinci, N.C. Bartelt, T.L. Einstein, Phys. Rev. Lett. 54, 14 (1985)

    Article  Google Scholar 

  22. R. Honmura, T. Kaneyoshi, J. Phys. C. 12, 3979 (1979)

    Article  ADS  Google Scholar 

  23. R.B. Griffiths, J. Math. Phys. 8, 478 (1967)

    Article  ADS  Google Scholar 

  24. R.B. Griffiths, J. Math. Phys. 8, 484 (1967)

    Article  ADS  Google Scholar 

  25. C.T. Lee, J. Math. Phys. 14, 1871 (1973)

    Article  ADS  Google Scholar 

  26. C.M. Newman, Z. Wahrscheintichkeitstheorie verw. Gebiete. 33, 75 (1975)

    Article  MATH  Google Scholar 

  27. J.L. Lebowitz, Phys. Lett. 36A, 99 (1971)

    Article  ADS  Google Scholar 

  28. B. Simon, Math. Phys. 77, 111 (1980)

    Article  ADS  Google Scholar 

  29. H.B. Callen, Phys. Lett. 4, 161 (1963)

    Article  MathSciNet  ADS  Google Scholar 

  30. L. Onsager, Phys. Rev. 65, 117 (1944)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  31. G.B. Taggart, Physica A. 113, 535 (1982)

    Article  ADS  Google Scholar 

  32. C.F. Baillie, R. Gupta, K.A. Hawick, G.S. Pawley, Phys. Rev. B. 45, 10438 (1992)

    Article  ADS  Google Scholar 

  33. F.C. Sá Barreto, M.L. O’Carroll, J. Phys. A. 16, 1035 (1983)

    Article  MathSciNet  ADS  Google Scholar 

Download references

Acknowledgments

JPS financial support from FAPEMIG/Brazil (No. 11.607- FAPEMIG/Brazil). FCSB is grateful to CAPES/Brazil (Project 00035115 (PVNS)-Capes/Brazil) for the financial support that made possible his visit to the UFSJ/Brazil.

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Authors and Affiliations

  1. Departamento de Matemática - UFSJ, Caixa Postal 110, 30301-160, São João del-Rei, MG, Brazil

    Jander P. Santos

  2. Departamento de Física - UFMG, Caixa Postal 1621, 30161-970, Belo Horizonte, MG, Brazil

    F. C. Sá Barreto

Authors
  1. Jander P. Santos
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  2. F. C. Sá Barreto
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Correspondence to Jander P. Santos.

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Santos, J.P., Barreto, F.C.S. Upper Bounds on the Critical Temperature of the Ashkin-Teller Model. Braz J Phys 46, 70–77 (2016). https://doi.org/10.1007/s13538-015-0385-0

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  • DOI: https://doi.org/10.1007/s13538-015-0385-0

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