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Moscow University Physics Bulletin

, Volume 74, Issue 2, pp 186–190 | Cite as

Classification of Phenomenological Models of Phase Transitions with Three-Component Order Parameters by Methods of Catastrophe Theory: \(L = {T_d}(\bar 43m)\)

  • S. V. PavlovEmail author
Physics of Condensed State of Matter
  • 3 Downloads

Abstract

Using the equivariant catastrophe theory, we classify phenomenological models of phase transitions with a three-component order parameter and with a number of control parameters from one to four. The analysis of phase diagrams of the obtained models shows that the description of all low-symmetry phases requires fewer terms of the power-series expansion than that required by the model constructed using the traditional method taking all terms up to the 2nth power into account (n > 1). The theoretical temperature dependence of the heat capacity is compared with the experimental data in the GaV4S8 compound.

Keywords

phase transitions phenomenological model catastrophe theory equivariant vector fields phase diagram 

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References

  1. 1.
    A. A. Mukovnin and V. M. Talanov, Solid State Commun. 182, 1 (2014).CrossRefGoogle Scholar
  2. 2.
    A. A. Mukovnin and V. M. Talanov, Eur. Phys. J. B 87, 34 (2014).CrossRefGoogle Scholar
  3. 3.
    A. A. Mukovnin and V. M. Talanov, Russ. J. Phys. Chem. A 88, 1478 (2014).CrossRefGoogle Scholar
  4. 4.
    S. Geller, Phys. Rev. B 14, 4345 (1976).CrossRefGoogle Scholar
  5. 5.
    A. C. Lawson, A. C. Larson, R. B. V. Dreele, et al., J. Less-Common Met. 132, 229 (1987).CrossRefGoogle Scholar
  6. 6.
    F. Kubel, Ferroelectrics 160, 61 (1994).CrossRefGoogle Scholar
  7. 7.
    P. W. Richter and C. W. F. T. Pistorius, J. Solid State Chem. 5, 276 (1972).CrossRefGoogle Scholar
  8. 8.
    V. I. Arnol’d, Russ. Math. Surv. 30 (5), 1 (1975).CrossRefGoogle Scholar
  9. 9.
    V. I. Arnold, S. M. Gusein-Zade, and A. N. Varchenko, Singularities of Differentiable Maps, Vol. 1: The Classification of Critical Sets, Caustics and Wave Fronts (Nauka, Moscow, 1982; Birkhäuser, 1985).zbMATHGoogle Scholar
  10. 10.
    E. I. Kut’in, V. L. Lorman, and S. V. Pavlov, Sov. Phys. Usp. 34, 497 (1991).CrossRefGoogle Scholar
  11. 11.
    S. V. Pavlov, Catastrophe Theory Methods in the Study of Phase Transitions (Mosk. Gos. Univ., Moscow, 1993).Google Scholar
  12. 12.
    S. V. Pavlov, Moscow Univ. Phys. Bull. 71, 202 (2016). doi  https://doi.org/10.3103/S0027134916020077 CrossRefGoogle Scholar
  13. 13.
    Yu. M. Gufan, Structural Phase Transitions (Nauka, Moscow, 1982).Google Scholar
  14. 14.
    T M. Izotova, A. P. Shamshin, and E. V. Matyushkin, in Computer Applications in Scientific Research (Moscow, 2004). http://www.ivtn.ru/2004/physmath/enter/r_pdf/dp04_30.pdf.
  15. 15.
    S. V. Pavlov, Moscow Univ. Phys. Bull. 71, 508 (2016). doi  https://doi.org/10.3103/S0027134916050155 CrossRefGoogle Scholar
  16. 16.
    A. P. Shamshin, T. M. Izotova, E. V. Matyushkin, and A. V. Desyatnichenko, Bull. Russ. Acad. Sci.: Phys. 68, 1061 (2004).Google Scholar
  17. 17.
    D. A. Cox, J. Little, and D. Oshea, Ideals, Varieties, and Algorithms (Springer, New York, 2007).CrossRefGoogle Scholar
  18. 18.
    T. Poston and I. Stewart, Catastrophe Theory and Its Applications (Pitman, 1978).Google Scholar
  19. 19.
    R. Gilmore, Catastrophe Theory for Scientists and Engineers (Wiley, 1981).Google Scholar
  20. 20.
    V. I. Arnol’d, Catastrophe Theory (Nauka, Moscow, 1990; Springer, 2004).zbMATHGoogle Scholar
  21. 21.
    E. Ruff, S. Widmann, P. Lunkenheimer, et al., arXiv: 1504.00309 [cond-mat.str-el].Google Scholar
  22. 22.
    D. Bichler, H. Slavik, and D. Johrendt, Z. Naturforsch. B 64, 915 (2009).CrossRefGoogle Scholar
  23. 23.
    D. Bichler, H. Slavik, D. Johrendt, et al., Phys. Rev. B 77, 212102 (2008).CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Department of PhysicsMoscow State UniversityMoscowRussia

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