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On critical behavior of phase transitions in certain antiferromagnets with complicated ordering

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Abstract

Within the four-loop ε expansion, we study the critical behavior of certain antiferromagnets with complicated ordering. We show that an anisotropic stable fixed point governs the phase transitions with new critical exponents. This is supported by the estimate of critical dimensionality N C c =1.445(20) obtained from six loops via the exact relation N C c =1/2N R c established for the complex and real hypercubic models.

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References

  1. D. Mukamel, Phys. Rev. Lett. 34, 481 (1975); D. Mukamel and S. Krinsky, J. Phys. C 8, L496 (1975); Phys. Rev. B 13, 5065 (1976).

    Article  ADS  Google Scholar 

  2. P. Bak and D. Mukamel, Phys. Rev. B 13, 5086 (1976).

    Article  ADS  Google Scholar 

  3. S. A. Brazovskii and I. E. Dzyaloshinskii, Pis’ma Zh. Éksp. Teor. Fiz. 21, 360 (1975) [JETP Lett. 21, 164 (1975)]; S. A. Brazovskii, I. E. Dzyaloshinskii, and B. G. Kukharenko, Zh. Éksp. Teor. Fiz. 70, 2257 (1976) [Sov. Phys. JETP 43, 1178 (1976)]; P. Bak, S. Krinsky, and D. Mukamel, Phys. Rev. Lett. 36, 52 (1976) and references therein.

    Google Scholar 

  4. D. Mukamel and S. Krinsky, Phys. Rev. B 13, 5078 (1976).

    ADS  Google Scholar 

  5. J. C. Toledano, L. Michel, P. Toledano, and E. Brézin, Phys. Rev. B 31, 7171 (1985).

    Article  ADS  MathSciNet  Google Scholar 

  6. J. Als-Nielsen, in Phase Transitions and Critical Phenomena, Ed. by C. Domb and M. S. Green (Academic, New York, 1976), Vol. 5A, p. 88.

    Google Scholar 

  7. R. Pynn and J. D. Axe, J. Phys. C 9, L199 (1976).

    Article  ADS  Google Scholar 

  8. J. Schneck et al., Phys. Rev. B 25, 1766 (1982).

    Article  ADS  Google Scholar 

  9. N. A. Shpot, Phys. Lett. A 133, 125 (1988); 142, 474 (1989).

    Article  ADS  Google Scholar 

  10. K. B. Varnashev and A. I. Sokolov, Fiz. Tverd. Tela (St. Petersburg) 38, 3665 (1996) [Phys. Solid State 38, 1996 (1996)]; A. I. Sokolov, K. B. Varnashev, and A. I. Mudrov, Int. J. Mod. Phys. B 12, 1365 (1998); A. I. Sokolov and K. B. Varnashev, Phys. Rev. B 59, 8363 (1999).

    Google Scholar 

  11. K. De’Bell and D. J. W. Geldart, Phys. Rev. B 32, 4763 (1985); E. J. Blagoeva, Mod. Phys. Lett. B 10, 439 (1996).

    ADS  Google Scholar 

  12. A. I. Mudrov and K. B. Varnashev, Phys. Rev. B 57, 3562 (1998); 57, 5704 (1998).

    ADS  Google Scholar 

  13. D. E. Khmelnitskii, Zh. Éksp. Teor. Fiz. 68, 1960 (1975) [Sov. Phys. JETP 41, 981 (1976)].

    Google Scholar 

  14. J. Sak, Phys. Rev. B 10, 3957 (1974); K. A. Cowley and A. D. Bruce, J. Phys. C 11, 3577 (1978).

    Article  ADS  Google Scholar 

  15. I. E. Dzyaloshinskii, Zh. Éksp. Teor. Fiz. 72, 1930 (1977) [Sov. Phys. JETP 45, 1014 (1977)].

    Google Scholar 

  16. A. Aharony, in Phase Transition and Critical Phenomena, Ed. by C. Domb and M. S. Green (Academic, New York, 1976), Vol. 6, p. 357.

    Google Scholar 

  17. G. ’t Hooft and M. Veltman, Nucl. Phys. B 44, 189 (1972); G. ’t Hooft, Nucl. Phys. B 61, 455 (1973).

    ADS  MathSciNet  Google Scholar 

  18. J. C. Le Guillou and J. Zinn-Justin, Phys. Rev. Lett. 39, 95 (1977); Phys. Rev. B 21, 3976 (1980); R. Seznec and J. Zinn-Justin, J. Math. Phys. 20, 1398 (1979); A. A. Vladimirov, D. I. Kazakov, and O. V. Tarasov, Zh. Éksp. Teor. Fiz. 77, 1035 (1979) [Sov. Phys. JETP 50, 521 (1979)].

    ADS  Google Scholar 

  19. J. M. Carmona, A. Pelissetto, and E. Vicari, Phys. Rev. B 61, 15136 (2000).

    Google Scholar 

  20. A. I. Mudrov and K. B. Varnashev, Phys. Rev. E 58, 5371 (1998); in Problems of Quantum Field Theory (Joint Inst. for Nuclear Research, Dubna, 1999), p. 267; hep-th/9811125 (1998).

    Article  ADS  Google Scholar 

  21. A. I. Mudrov and K. B. Varnashev, J. Phys. A 34, L347 (2001); in Group Theoretical Methods in Physics (Joint Inst. for Nuclear Research, Dubna, 2001); cond-mat/0011167 (2000).

    Article  ADS  Google Scholar 

  22. H. Kleinert and V. Schulte-Frohlinde, Phys. Lett. B 342, 284 (1995).

    ADS  Google Scholar 

  23. K. B. Varnashev, J. Phys. A 33, 3121 (2000); Phys. Rev. B 61, 14660 (2000).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  24. R. Folk, Yu. Holovatch, and T. Yavors’kii, Phys. Rev. B 62, 12195 (2000).

    Google Scholar 

  25. A. Pelissetto and E. Vicari, cond-mat/0012164 (2000).

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Authors and Affiliations

  1. Bar-Ilan University, 52900, Ramat-Gan, Israel

    A. I. Mudrov

  2. St. Petersburg Electrotechnical University, St. Petersburg, 197376, Russia

    K. B. Varnashev

Authors
  1. A. I. Mudrov
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  2. K. B. Varnashev
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Additional information

From Pis’ma v Zhurnal Éksperimental’no\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) i Teoretichesko\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) Fiziki, Vol. 74, No. 5, 2001, pp. 309–313.

Original English Text Copyright © 2001 by Mudrov, Varnashev.

This article was submitted by the authors in English.

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Mudrov, A.I., Varnashev, K.B. On critical behavior of phase transitions in certain antiferromagnets with complicated ordering. Jetp Lett. 74, 279–283 (2001). https://doi.org/10.1134/1.1417166

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  • DOI: https://doi.org/10.1134/1.1417166

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