Critical properties of the anisotropic Ising model with competing interactions

Order, Disorder, and Phase Transition in Condensed System

Abstract

The critical properties of the anisotropic Ising model with competing interactions have been investigated by Monte Carlo methods. The region of localization of the Lifshitz point on the phase diagram has been computed. Relations of the finite-size scaling theory are used to calculate the critical exponents of the heat capacity, susceptibility, and magnetization at various values of the competing interaction parameter J1. A crossover to a critical behavior characteristic of a multicritical point with increasing parameter J1 is shown to be present in the system.

References

  1. 1.
    A. K. Murtazaev, I. K. Kamilov, and M. A. Magomedov, Zh. Eksp. Teor. Fiz. 120(6), 1535 (2001) [JETP 93 (6), 1330 (2001)].Google Scholar
  2. 2.
    P. Peczak and D. P. Landau, Phys. Rev. B: Condens. Matter 43, 1048 (1991); Phys. Rev. B: Condens. Matter 47, 14260 (1993).ADSCrossRefGoogle Scholar
  3. 3.
    I. K. Kamilov, A. K. Murtazaev, and Kh. K. Aliev, Usp. Fiz. Nauk 169(7), 773 (1999) [Phys.—Usp. 42 (7), 689 (1999)].CrossRefGoogle Scholar
  4. 4.
    Yu. A. Izyumov, Neutron Diffraction on Long-Period Modulated Structures (Energoatomizdat, Moscow, 1987) [in Russian].Google Scholar
  5. 5.
    W. Selke, Phys. Rep. 170, 213 (1988).MathSciNetADSCrossRefGoogle Scholar
  6. 6.
    B. Neubert, M. Pleimling, and R. Siems, Ferroelectrics 141, 208 (1998).Google Scholar
  7. 7.
    W. Selke, Phys. Rep. 170, 213 (1988).MathSciNetADSCrossRefGoogle Scholar
  8. 8.
    R. J. Elliott, Phys. Rev. 124, 346 (1961).ADSCrossRefGoogle Scholar
  9. 9.
    J. Yeomans, E. Henry, and T. David, Solid State Phys. 41, 151 (1988).CrossRefGoogle Scholar
  10. 10.
    W. Selke, in Phase Transitions and Critical Phenomena, Ed. by C. Domb and J. L. Lebowitz (Academic, London, 1992), Vol. 15, p. 254.Google Scholar
  11. 11.
    W. Selke and M. E. Fisher, Phys. Rev. B: Condens. Matter 20, 257 (1979).ADSCrossRefGoogle Scholar
  12. 12.
    R. M. Hornreich, M. Luban, and S. Shtrikman, Phys. Rev. Lett. 35, 1678 (1975).ADSCrossRefGoogle Scholar
  13. 13.
    T. Garel and P. Pfeuty, J. Phys. C: Solid State Phys. 9, L245 (1976).ADSCrossRefGoogle Scholar
  14. 14.
    S. Redner and H. E. Stanley, J. Phys. C: Solid State Phys. 10, 4765 (1977); Phys. Rev. B: Solid State 16, 4901 (1977).ADSCrossRefGoogle Scholar
  15. 15.
    M. E. Fisher and W. Selke, Philos. Trans. R. Soc. London, Ser. A 302, 1 (1981).MathSciNetADSCrossRefGoogle Scholar
  16. 16.
    W. Selke and P. M. Duxbury, Z. Phys. B: Condens. Matter 57, 49 (1984).ADSCrossRefGoogle Scholar
  17. 17.
    P. Bak and J. Boehm, Phys. Rev. B: Condens. Matter 21, 5297 (1980).ADSCrossRefGoogle Scholar
  18. 18.
    A. Surda, Phys. Rev. B: Condens. Matter 69, 134116 (2004).ADSCrossRefGoogle Scholar
  19. 19.
    A. Gendiar and T. Nishino, Phys. Rev. B: Condens. Matter 71, 024404 (2005).ADSCrossRefGoogle Scholar
  20. 20.
    W. Selke and M. E. Fisher, J. Magn. Magn. Mater. 15–18, 403 (1980).CrossRefGoogle Scholar
  21. 21.
    E. B. Rasmussen and S. J. Knak-Jensen, Phys. Rev. B: Condens. Matter 24, 2744 (1981).ADSCrossRefGoogle Scholar
  22. 22.
    K. Kaski and W. Selke, Phys. Rev. B: Condens. Matter 31, 3128 (1985).ADSCrossRefGoogle Scholar
  23. 23.
    M. Pleimling and M. Henkel, Phys. Rev. Lett. 87, 125702 (2001).ADSCrossRefGoogle Scholar
  24. 24.
    J. Oitmaa, J. Phys. A: Math. Gen. 18, 365 (1985).ADSCrossRefGoogle Scholar
  25. 25.
    Z. Mo and M. Ferer, Phys. Rev. B: Condens. Matter 43, 10890 (1991).ADSCrossRefGoogle Scholar
  26. 26.
    M. Henkel and M. Pleimling, Comput. Phys. Commun. 147, 161 (2002).CrossRefGoogle Scholar
  27. 27.
    M. Shpot and H. W. Diehl, Nucl. Phys. B 612, 340 (2001).ADSMATHCrossRefGoogle Scholar
  28. 28.
    Y. Muraoka, T. Kasama, and T. Idogaki, J. Magn. Magn. Mater. 272, E995 (2004).ADSCrossRefGoogle Scholar
  29. 29.
    W. Selke, Z. Phys. B: Condens. Matter 29, 133 (1978).ADSGoogle Scholar
  30. 30.
    U. Wolf, Phys. Rev. Lett. 62, 361 (1989).ADSCrossRefGoogle Scholar
  31. 31.
    K. Binder and D. W. Heermann, Monte Carlo Simulation in Statistical Physics: An Introduction (Springer, Berlin, 1979; Nauka, Moscow, 1980).Google Scholar
  32. 32.
    A. K. Murtazaev and Zh. G. Ibaev, Fiz. Nizk. Temp. (Kharkov) 35(10), 1011 (2009) [Low Temp. Phys. 35 (10), 792 (2009)].Google Scholar
  33. 33.
    P. Peczak, A. M. Ferrenberg, and D. P. Landau, Phys. Rev. 43, 6097 (1991).Google Scholar
  34. 34.
    S. A. Antonenko and A. I. Sokolov, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 51, 1894 (1995).CrossRefGoogle Scholar
  35. 35.
    J. J. C. La Gulluo and J. Zinn-Justin, J. Phys., Lett. 46, L137 (1985).CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  1. 1.Amirkhanov Institute of Physics, Dagestan Scientific CenterRussian Academy of SciencesMakhachkalaRussia
  2. 2.Dagestan State UniversityMakhachkalaRussia

Personalised recommendations