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Critical properties of the antiferromagnetic layered Ising model on a cubic lattice with competing interactions

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Abstract

The critical properties of the antiferromagnetic layered Ising model on a cubic lattice with regard to the nearest-neighbor and next-nearest-neighbor interactions are investigated by the Monte Carlo method using the replica algorithm. The investigations are carried out for the ratios of exchange nearest-neighbor and next-nearest-neighbor interactions r = J 2/J 1 in the range of 0 ≤ r ≤ 1.0. Using the finite-size scaling theory, the static critical indices of specific heat α, order parameter β, susceptibility γ, correlation radius ν, and Fisher index η are calculated. It is shown that the universality class of the critical behavior of this model is retained in the range of 0 ≤ r ≤ 0.4. It is established that the change in the next-nearest-neighbor interaction value in this model in the range of r > 0.8 leads to the same universality class as the three-dimensional fully frustrated Ising model on the cubic lattice.

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References

  1. V. S. Dotsenko, Phys. Usp. 38, 457 (1995).

    Article  ADS  Google Scholar 

  2. S. E. Korshunov, Phys. Usp. 49, 225 (2006).

    Article  ADS  Google Scholar 

  3. A. Malakis, P. Kalozoumis, and N. Tyraskis, Eur. Phys. J. B 50, 63 (2006).

    Article  ADS  Google Scholar 

  4. D. P. Landau and K. Binder, Monte Carlo Simulations in Statistical Physics (Cambridge Univ. Press, Cambridge, 2000), p. 384.

    MATH  Google Scholar 

  5. F. A. Kassan-Ogly, B. N. Filippov, A. K. Murtazaev, M. K. Ramazanov, and M. K. Badiev, J. Magn. Magn. Mater. 324, 3418 (2012).

    Article  ADS  Google Scholar 

  6. A. K. Murtazaev, M. K. Ramazanov, and M. K. Badiev, J. Low Temp. Phys. 37, 1001 (2011).

    Article  Google Scholar 

  7. K. Binder and D. P. Landau, Phys. Rev. B 21, 1941 (1980).

    Article  ADS  Google Scholar 

  8. F. A. Kassan-Ogly, A. K. Murtazaev, A. K. Zhuravlev, M. K. Ramazanov, and A. I. Proshkin, J. Magn. Magn. Mater. 384, 247 (2015).

    Article  ADS  Google Scholar 

  9. A. K. Murtazaev, M. K. Ramazanov, F. A. Kassan-Ogly, and M. K. Badiev, J. Exp. Theor. Phys. 117, 1091 (2013).

    Article  Google Scholar 

  10. A. Kalz and A. Honecker, Phys. Rev. B 86, 134410 (2012).

    Article  ADS  Google Scholar 

  11. S. Jin, A. Sen, and A. W. Sandvik, Phys. Rev. Lett. 108, 045702 (2012).

    Article  ADS  Google Scholar 

  12. S. Jin, A. Sen, W. Guo, and A. W. Sandvik, Phys. Rev. B 87, 144406 (2013).

    Article  ADS  Google Scholar 

  13. R. J. Baxter, Exactly Solved Models in Statistical Mechanics (Academic, New York, 1982).

    MATH  Google Scholar 

  14. M. K. Ramazanov and A. K. Murtazaev, JETP Lett. 101, 714 (2015).

    Article  ADS  Google Scholar 

  15. M. K. Ramazanov and A. K. Murtazaev, JETP Lett. 103, 460 (2016).

    Article  ADS  Google Scholar 

  16. A. R. dos Anjos, J. R. Viana, J. R. de Sousa, and J. A. Plascak, Phys. Rev. E 76, 022103 (2007).

    Article  ADS  Google Scholar 

  17. D. R. O. Salmon, N. Crokidakis, A. M. Neto, T. I. Padilha, J. R. Viana, and J. R. de Sousa, Int. J. Mod. Phys. B 27, 1350162 (2013).

    Article  ADS  Google Scholar 

  18. A. K. Murtazaev, M. K. Ramazanov, and M. K. Badiev, Phys. Solid State 52, 1673 (2010).

    Article  ADS  Google Scholar 

  19. A. K. Murtazaev and M. K. Ramazanov, Phys. Solid State 53, 1067 (2011).

    Article  ADS  Google Scholar 

  20. A. K. Murtazaev, M. K. Ramazanov, and M. K. Badiev, J. Exp. Theor. Phys. 115, 303 (2012).

    Article  ADS  Google Scholar 

  21. A. K. Murtazaev, M. K. Ramazanov, and M. K. Badiev, Physica B 476, 1 (2015).

    Article  ADS  Google Scholar 

  22. M. K. Ramazanov, A. K. Murtazaev, and M. A. Magomedov, Solid State Commun. 233, 35 (2016).

    Article  ADS  Google Scholar 

  23. M. K. Badiev, A. K. Murtazaev, and M. K. Ramazanov, J. Exp. Theor. Phys. 123, 623 (2016).

    Article  ADS  Google Scholar 

  24. A. K. Murtazaev, M. K. Ramazanov, D. R. Kurbanova, M. K. Badiev, and Ya. K. Abuev, Phys. Solid State 59, 1103 (2017).

    Article  ADS  Google Scholar 

  25. A. Mitsutake, Y. Sugita, and Y. Okamoto, Biopolymers (Peptide Sci.) 60, 96 (2001).

    Article  Google Scholar 

  26. F. Wang and D. P. Landau, Phys. Rev. Lett. 86, 2015 (2001).

    Google Scholar 

  27. K. Binder and J.-Sh. Wang, J. Stat. Phys. 55, 87 (1989).

    Article  ADS  Google Scholar 

  28. K. Binder and D. W. Heermann, Monte Carlo Simulation in Statistical Physics (Springer, Berlin, 1988, Nauka, Moscow, 1995), p. 214.

    MATH  Google Scholar 

  29. A. E. Ferdinand and M. E. Fisher, Phys. Rev. 185, 832 (1969).

    Article  ADS  Google Scholar 

  30. M. E. Fisher and M. N. Barber, Phys. Rev. Lett. 28, 1516 (1972).

    Article  ADS  Google Scholar 

  31. P. Peczak, A. M. Ferrenberg, and D. P. Landau, Phys. Rev. B 43, 6087 (1991).

    Article  ADS  Google Scholar 

  32. Ch. Holm and W. Janke, Phys. Rev. B 48, 936 (1993).

    Article  ADS  Google Scholar 

  33. J. C. le Guillou and J. Zinn-Justin, Phys. Rev. B 21, 3976 (1980).

    Article  ADS  MathSciNet  Google Scholar 

  34. H. T. Diep, P. Lallemand, and O. Nagai, J. Phys. C 18, 1067 (1985).

    Article  ADS  Google Scholar 

  35. L. W. Bernardi, K. Hukushima, and H. Takayama, J. Phys. A 32, 1787 (1999).

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Amirkhanov Institute of Physics, Dagestan Scientific Center, Russian Academy of Sciences, Makhachkala, Dagestan, 367003, Russia

    A. K. Murtazaev & M. K. Ramazanov

  2. Dagestan State University, Makhachkala, Dagestan, 367008, Russia

    A. K. Murtazaev

Authors
  1. A. K. Murtazaev
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  2. M. K. Ramazanov
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Correspondence to M. K. Ramazanov.

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Original Russian Text © A.K. Murtazaev, M.K. Ramazanov, 2017, published in Fizika Tverdogo Tela, 2017, Vol. 59, No. 9, pp. 1797–1803.

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Murtazaev, A.K., Ramazanov, M.K. Critical properties of the antiferromagnetic layered Ising model on a cubic lattice with competing interactions. Phys. Solid State 59, 1822–1828 (2017). https://doi.org/10.1134/S1063783417090219

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  • DOI: https://doi.org/10.1134/S1063783417090219

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