Geodesic
Singularities of the thermodynamic potential under second-order
Teoretičeskaâ i matematičeskaâ fizika, Tome 157 (2008) no. 2, pp. 273-285 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

[1] B. A. Strukov, A. P. Levanyuk, Fizicheskie osnovy segnetoelektricheskikh yavlenii v kristallakh, Nauka, M., 1983 | Zbl

[2] A. P. Levanyuk, A. R. Pogosyan, E. M. Uyukin, DAN SSSR, 256:1 (1961), 60 | MR

[3] L. D. Landau, E. M. Lifshits, Teoreticheskaya fizika T. V. Statisticheskaya fizika, Nauka, M., 1976 | MR | MR | Zbl

[4] V. L. Ginzburg, FTT, 2:9 (1960), 2031–2134

[5] L. Onsager, Phys. Rev., 65:3–4 (1944), 117–149 | DOI | MR | Zbl

[6] A. Z. Patashinskii, V. L. Pokrovskii, Fluktuatsionnaya teoriya fazovykh perekhodov, Nauka, M., 1975 | MR | MR

[7] V. I. Altukhov, B. A. Strukov, “Kriticheskoe rasseyanie nositelei i teorii anomalnogo teplovogo i elektricheskogo soprotivleniya v segnetoelektrikakh”, Sb. tezisov dokl. XVI Vserossiiskoi konferentsii po fizike segnetoelektrikov (Tver, 17–21 sentyabrya 2002 g.), Tver, 2002, 62

[8] V. M. Fridkin, Segnetoelektriki-poluprovodniki, Nauka, M., 1976

[9] Ya. G. Girshberg, V. I. Tamarchenko, FTT, 18:4 (1976), 1066–1072

[10] E. V. Bursian, Ya. G. Girschberg, V. I. Tamarchenko, Ferroelectrics, 18 (1978), 39–43 | DOI

[11] E. V. Bursian, Ya. G. Girshberg, Kogerentnye effekty v segnetoelektrikakh, Prometei, M., 1989

[12] A. A. Abrikosov, L. P. Gorkov, I. E. Dzyaloshinskii, Metody kvantovoi teorii polya v statisticheskoi fizike, Fizmatgiz, M., 1962 | MR | MR | Zbl

[13] E. N. Myasnikov, A. E. Myasnikova, Z. P. Mastropas, ZhETF, 129:3 (2006), 548–565