Skip to main content
SpringerLink
Log in

Phase diagrams and magnetization curves of the mixed Ashkin–Teller model including metastable and unstable states

  • Regular Article - Statistical and Nonlinear Physics
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

We investigate the magnetic properties of a mixed Ashkin–Teller model (spin-1/2 and spin-1) in a square lattice, under the effect of a crystal field, using the mean-field theory. Phase diagrams, magnetizations and free energy curves are presented. Besides the stable states of the order parameters, we also obtain the metastable and unstable states, which are shown in the phase diagrams and magnetization curves. The classification of the stable, metastable and unstable states is made by comparing their free-energy values.

Graphic abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: This is a theoretical work in which all the important data is already present.]

References

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

    Article  ADS  Google Scholar 

  2. M. Sluiter, Y. Kawazoe, Sci. Rep. Inst. Tokohu Univ. A 40, 301 (1995)

    Google Scholar 

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

    Article  ADS  Google Scholar 

  4. P. Bak, P. Kleban, W.N. Unertel, J. Ochab, G. Akinci, N.C. Barlet, T.L. Einstein, Phys. Rev. Lett. 54, 1542 (1985)

    ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  6. Ü. Akinci, Phys. A 469, 740 (2017)

    Article  MathSciNet  Google Scholar 

  7. P.L. Christiano, S.G. Rosa, Phys. Rev. A 34, 730 (1986)

    Article  ADS  Google Scholar 

  8. J.P. Santos, D.S. Rosa, F.C.S. Barreto, Phys. Lett. A 382, 272 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  9. J.P. Santos, J.A.J. Avila, D.S. Rosa, R.M. Francisco, J. Magn. Magn. Mater. 469, 35 (2019)

    Article  ADS  Google Scholar 

  10. J.P. Santos, F.C.S. Barreto, J. Magn. Magn. Mater. 401, 724 (2016)

    Article  ADS  Google Scholar 

  11. J.P. Santos, F.C.S. Barreto, Phys. A 421, 316 (2015)

    Article  Google Scholar 

  12. J.P. Santos, F.C.S. Barreto, Braz. J. Phys. 46, 70 (2016)

    Article  ADS  Google Scholar 

  13. J.A. Plascak, F.C.S. Barreto, Phys. A 19, 2195 (1986)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  15. P. Pawlicki, G. Musial, G. Kamieniarz, L. Debski, Phys. A 242, 281 (1997)

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  18. Z. Wojtkowiak, G. Musial, J. Magn. Magn. Mater. 500, 166365 (2020)

    Article  Google Scholar 

  19. D. Jeziorek-Kniola, Z. Wojtkowiak, G. Musial, Comput. Methods. Sci. Technol. 25, 31 (2019)

    Article  Google Scholar 

  20. D. Jeziorek-Kniola, Z. Wojtkowiak, G. Musial, Acta Phys. Polo. A 133, 435 (2018)

    Article  ADS  Google Scholar 

  21. Z. Wojtkowiak, G. Musial, Phys. A 513, 104 (2019)

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  26. M. Blume, Phys. Rev. 141, 517 (1966)

    Article  ADS  Google Scholar 

  27. H.W. Capel, Physica (Amsterdam) 32, 966 (1966)

    Article  ADS  Google Scholar 

  28. H.W. Capel, Physica (Amsterdam) 33, 295 (1967)

    Article  ADS  Google Scholar 

  29. H.W. Capel, Physica (Amsterdam) 37, 423 (1967)

    Article  ADS  Google Scholar 

  30. K.N. Kudin, G.E. Scuseria, R.L. Martin, Phys. Rev. Lett. 89, 266402 (2002)

    Article  ADS  Google Scholar 

  31. N. Lanata, Y. Yao, X. Deng, V. Dobrosavljevic, G. Kotliar, Phys. Rev. Lett. 118, 126401 (2017)

    Article  ADS  Google Scholar 

  32. M. Blume, V.J. Emery, R.B. Griffiths, Phys. Rev. A 4, 1071 (1971)

    Article  ADS  Google Scholar 

  33. I.D. Lawrie, S. Sarbach, Chapter 1: Theory of Tricritical Points . in Phase Transitions and Critical Phenomena, vol. 9, ed. by: C. Domb, J.L. Lebowitz (Academic, London, 1984), pp. 2–155

  34. N.B. Wilding, P. Nielaba, Phys. Rev. E 53, 926 (1996)

    Article  ADS  Google Scholar 

  35. M. Jaime et al., Nat. Commun. 8, 99 (2017)

    Article  ADS  Google Scholar 

  36. N.G. Fytas, J. Zierenberg, P.E. Theodorakis, M. Weigel, W. Janke, A. Malakis, Phys. Rev. E 97, 040102 (2018)

    Article  ADS  Google Scholar 

  37. E. Vatansever, Z.D. Vatansever, P.E. Theodorakis, N.G. Fytas, Phys. Rev. E 102, 062138 (2020)

    Article  ADS  Google Scholar 

  38. R.M. Francisco, J.J. Carvalho, G.Y. Oyadomari, J.P. Santos, Phys. A 531, 121819 (2019)

    Article  MathSciNet  Google Scholar 

  39. M. Loulidi, Phys. Rev. B 55, 17 (1997)

    Article  Google Scholar 

  40. M. Badehdah, S. Bekhechi, A. Benyoussef, B. Ettaki, Phys. Rev. B 59, 6250 (1999)

    Article  ADS  Google Scholar 

  41. P. Ndizeye, F. Hontinfinde, B. Kounouhewa, S. Bekhechi, Cent. Eur. J. Phys. 12, 375 (2014)

    Google Scholar 

  42. R. Boudefla, S. Bekhechi, F. Hontinfinde, Condens. Mater. Phys. 18, 33703 (2015)

    Article  Google Scholar 

  43. V.M. Rozenbaum, JETP Lett. 78, 34 (2003)

    Article  ADS  Google Scholar 

  44. T. Horiguchi, Y. Honda, Prog. Theor. Phys. 93, 981 (1995)

    Article  ADS  Google Scholar 

  45. Z. Amimer, S. Bekhechi, B.N. Brahmi, R. Boude, H. Ez-Zahraouy, A. Rachadi, Condens. Mater. Phys. 23, 33707 (2020)

    Article  Google Scholar 

  46. S. Bekhechi, A. Benyoussef, A. El-Kenz, B. Ettaki, M. Loulidi, Eur. Phys. J. B 18, 275 (2000)

    Article  ADS  Google Scholar 

  47. H. Jones, Rapid Solidification of Metals and Alloys (Institution of Metallurgists, London, 1982)

    Google Scholar 

  48. F. Spaepen, A. I. Taub, Chapter 13: Flow and fracture. in Amorphous metallic alloy, single volume, ed. by F.E. Luborsky (Butterworths, London, 1983), pp. 231–256

  49. R. L. Ashbrook (ed.), Rapid solidification technology - source book (American Society for Metals, Metals Park, Ohio, 1983)

  50. J.D. Gunton, M. Droz, Introduction to the Theory of Metastable and Unstable States (Springer, Berlin, 1983)

    Book  Google Scholar 

  51. J. D. Gunton, M. San Miguel, P.S. Sahni, Chapter 3: The dynamics of first-order phase transition. in Phase Transitions and Critical Phenomena, vol. 8, ed. by: C. Domb, J.L. Lebowitz (Academic Press, New York, 1983), pp. 269–467

  52. C. Ekiz, M. Keskin, O. Yalçin, Phys. A 293, 215 (2001)

    Article  Google Scholar 

  53. J.P. Santos, F.C.S. Barreto, D.S. Rosa, J. Magn. Magn. Mater. 423, 175 (2017)

    Article  ADS  Google Scholar 

  54. C. Ekiz, M. Keskin, Phys. Rev. B 66, 054105 (2002)

    Article  ADS  Google Scholar 

  55. R.G.B. Mendes, F.C.S. Barreto, J.P. Santos, Braz. J. Phys. 48, 137 (2018)

    Article  ADS  Google Scholar 

  56. R.G.B. Mendes, F.C.S. Barreto, J.P. Santos, Phys. A 505, 1186 (2018)

    Article  MathSciNet  Google Scholar 

  57. N.N. Bogoliubov, J. Phys. (USSR) 11, 23 (1947)

    Google Scholar 

Download references

Acknowledgements

R. M. F. acknowledges financial support from FAPEMIG/Brazil (No. 11608—FAPEMIG/Brazil). J. P. S. would like to thank the Brazilian agencies CNPq (No. 306404/2019-2) for financial support.

Author information

Authors and Affiliations

  1. Departamento de Ciências Naturais, Universidade Federal de São João del-Rei, C.P. 110, São João del-Rei, MG, 36301-160, Brazil

    J. P. Santos, G. B. B. Nascimento, K. L. A. Resende & R. M. Francisco

  2. Departamento de Matemática, Universidade Federal de São João del-Rei, C.P. 110, São João del-Rei, MG, 36301-160, Brazil

    J. P. Santos

Authors
  1. J. P. Santos
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. B. B. Nascimento
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. K. L. A. Resende
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. R. M. Francisco
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. M. Francisco.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Santos, J.P., Nascimento, G.B.B., Resende, K.L.A. et al. Phase diagrams and magnetization curves of the mixed Ashkin–Teller model including metastable and unstable states. Eur. Phys. J. B 94, 136 (2021). https://doi.org/10.1140/epjb/s10051-021-00143-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/s10051-021-00143-6

Search

Navigation