Role of Fluctuations in the Coherent Displacements of Atomic Equilibrium Positions at Second-Order Phase Transitions

  • Z. P. Mastropas Southern Federal University
  • E. N. Myasnikov Southern Federal University
Keywords: thermodynamic potential, structure transformation, electron-phonon interaction, oscillation mode, wave function, deformation, Hamiltonian, Green function


Second-order phase transitions in ferroics of the ferroelastic type have been studied theoretically. The temperature-induced phase transition in crystals with a wide forbidden gap caused by the interaction between electrons and a branch of acoustic vibrations in the crystal lattice is considered. The vertex part of this interaction with transverse lattice vibrations is calculated. The characteristic features of the thermodynamic potential at the transition point and the temperature dependence of the acoustic phonon dispersion at the transition over quasiequilibrium states are discussed. It is shown that the stabilization of structure fluctuations by the electron subsystem in the high-symmetry phase, and a reduction of soft mode frequencies makes those fluctuations metastable.


  1. V.L. Bonch-Bruevich, Usp. Fiz. Nauk 56, 1 (1955).

  2. H. Haken, Quantum Field Theory of Solids (NorthHolland, Amsterdam, 1976).
  3. A.E. Myasnikova, E.N. Myasnikov, and Z.P. Mastropas, Theor. Mat. Phys. 157, 1595 (2008).

  4. L.D. Landau and E.M. Lifshitz, Statistical Physics, Part 1 (Pergamon Press, Oxford, 1980).
  5. A.Z. Patashinski and V.L. Pokrovsky, Fluctuation Theory of Phase Transitions (Pergamon Press, Oxford, 1982).
  6. V.L. Ginzburg, Fiz. Tverd. Tela 2, 2031 (1960).
  7. A.S. Davydov, Solid State Theory (Academic Press, New York, 1980).
  8. E.V. Bursian and Ya.G. Girshberg, Coherent Effects in Ferroelectrics (Prometei, Moscow, 1989) (in Russian).
  9. E.N. Myasnikov, A.E. Myasnikova, and Z.P. Mastropas, Zh. Eksp. Teor. Fiz. ` 129, 548 (2006).
  10. A.E.Myasnikova and E.N.Myasnikov, Phys. Rev. B 77, 165136 (2008).

  11. S.A. Gridnev, Soros. Obrazov. Zh. 8, 100 (2000).
  12. L. Onsager, Phys. Rev. 65, 117 (1944).

  13. J.R. Klauder and E.C.G. Sudarshan, Fundamentals of Quantum Optics (Benjamin, New York, 1968).
  14. V.A. Ryzhov, A.V. Lazuta, and V.P. Khalyavin, Solid State Commun. 103, 804 (2004).

How to Cite
Mastropas, Z., & Myasnikov, E. (2018). Role of Fluctuations in the Coherent Displacements of Atomic Equilibrium Positions at Second-Order Phase Transitions. Ukrainian Journal of Physics, 58(6), 573.
Solid matter