Abstract
Phenomenological models of phase transitions for two- and three-component order parameters are constructed by means of catastrophe theory using equivariant vector fields that consider the symmetry of the thermodynamic system. The models are classified according to the number of control parameters, depending on external thermodynamic conditions. Phase diagrams of some models are constructed and theoretical temperature dependences of their thermal properties are calculated. A comparison of theoretical and experimental data show a satisfactory match in quality.
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REFERENCES
Landau, L.D., Sobranie trudov (Collected Papers), Moscow: Nauka, 1967, vol. 1.
Kut’in, E.I., Lorman, V.L., and Pavlov, S.V., Sov. Phys. Usp., 1991, vol. 34, no. 10, p. 497.
Pavlov, S.V., Metody teorii katastrof v issledovaniyakh fazovykh perekhodov (Catastrophe Theory Methods in the Study of Phase Transitions), Moscow: Mosk. Gos. Univ., 1993.
Poston, T. and Stewart, I., Catastrophe Theory and Its Applications, Courier Corp., 1996.
Shirokov, V.B., Vestn. Yuzhn. Nauchn. Tsentra, 2012, vol. 8, no. 2, p. 3.
Arnol’d, V.I., Varchenko, A.N., and Gusein-Zade, S.M., Osobennosti differentsiruemykh otobrazhenii (Features of Differential Mappings), vol. 1: Klassifikatsiya kriticheskikh tochek, kaustik i volnovykh frontov (Classification of Critical Points, Caustics, and Wave Fronts), Moscow: Nauka, 1982.
Gufan, Yu.M., Strukturnye fazovye perekhody (Structural Phase Transitions), Moscow: Nauka, 1982.
Gufan, Yu.M. and Larin, E.S., Izv. Akad. Nauk SSSR, Ser. Fiz., 1979, vol. 43, no. 8, p. 1567.
Gufan, Yu.M. and Sakhnenko, V.P., Sov. Phys. JETP, 1973, vol. 36, no. 5, p. 1009.
Mukovnin, A.A. and Talanov, V.M., Russ. J. Phys. Chem. A, 2012, vol. 86, no. 12, p. 1785.
Shamshin, A.P., Izotova, T.M., Matyushkin, E.V., and Desyatnichenko, A.V., Bull. Rus. Acad. Sci.: Phys., 2004, vol. 68, no. 7, p. 1061.
Talanov, V.M., Shirokov, V.B., Torgashev, V.I., Berger, G.A., and Burtsev, V.A., Glass Phys. Chem., 2007, vol. 33, p. 596.
Kim, I., Jang, K., and Li, L., Phase Transitions, 2018, vol. 91, no. 3, p. 239.
Pavlov, S.V., Moscow Univ. Phys. Bull., 2016, vol. 71, no. 2, p. 202.
Pavlov, S.V., Moscow Univ. Phys. Bull., 2017, vol. 72, no. 6, p. 569.
Galam, S. and Hatch, D.M., Phys. Rev. B, 1986, vol. 34, no. 11, p. 7813.
D’yakonov, V.P., Markovich, V.I., Kovarskii, V.L., Markovich, A.V., Borowiec, M., Endzheichak, A., and Szymczak, G., Phys. Solid State, 1998, vol. 40, no. 12, p. 2017.
Mukovnin, A.A. and Talanov, V.M., Solid State Commun., 2014, vol. 182, no. 1, p. 1.
Ruff, E., Widmann, S., Lunkenheimer, P., et al., Sci. Adv., 2015, vol. 1, no. 10, p. e1500916.
Bichler, D., Slavik, H., and Johrendt, D., Z. Naturforsch. B, 2009, vol. 64, no. 8, p. 915.
Sergienko, I.A., Gufan, Yu.M., and Urazhdin, S., Phys. Rev. B, 2002, vol. 65, no. 14, p. 144104.
La-Orauttapong, D., Noheda, B., Ye, Z.-G., et al., Phys. Rev. B, 2002, vol. 65, no. 14, p. 144101.
Ye, Z.-G., Noheda, B., Dong, M., et al., Phys. Rev. B, 2001, vol. 64, no. 18, p. 184114.
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Translated by I. Obrezanova
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Pavlov, S.V. Constructing and Classifying Phenomenological Models of Phase Transitions by Means of Catastrophe Theory. Bull. Russ. Acad. Sci. Phys. 83, 1051–1061 (2019). https://doi.org/10.3103/S1062873819090193
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DOI: https://doi.org/10.3103/S1062873819090193