Geodesic
Singularities of the~thermodynamic potential under second-order
Teoretičeskaâ i matematičeskaâ fizika, Tome 157 (2008) no. 2, pp. 273-285

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We consider phase transitions in crystals with a strong interband electron–phonon interaction. We investigate the thermodynamic potential of the system using the method of temperature Green's functions, which takes quantum and thermal fluctuations into account. We show that in the absence of striction, these phase transitions are realized as a sequence of second-order phase transitions in each of which the thermodynamic potential has a logarithmic singularity, as in the Onsager model. This suggests that this singularity is characteristic of all second-order phase transitions. We show that the energy preference of the transition to the ordered phase is ensured by the electron coupling to coherent displacements of ions along normal coordinates of the phonon modes. We calculate the limit value of the energy decrease in the ordered phase compared with the symmetric phase as $T\to0$ K.
Keywords: thermodynamic potential, structure rearrangement, electron–phonon coupling
Mots-clés : vibration mode. 
@article{TMF_2008_157_2_a7,
     author = {A. E. Myasnikova and E. N. Myasnikov and Z. P. Mastropas},
     title = {Singularities of the~thermodynamic potential under second-order},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {273--285},
     publisher = {mathdoc},
     volume = {157},
     number = {2},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2008_157_2_a7/}
}
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A. E. Myasnikova; E. N. Myasnikov; Z. P. Mastropas. Singularities of the~thermodynamic potential under second-order. Teoretičeskaâ i matematičeskaâ fizika, Tome 157 (2008) no. 2, pp. 273-285. http://geodesic.mathdoc.fr/item/TMF_2008_157_2_a7/