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Reviews of topical problems

# The problem of phase transitions in statistical mechanics

Institute of Physical Chemistry, Russian Academy of Sciences, Leninsky prosp. 31, Moscow, 119991, Russian Federation

The first part of this review deals with the single-phase approach to the statistical theory of phase transitions. This approach is based on the assumption that a first-order phase transition is due to the loss of stability of the parent phase. We demonstrate that it is practically impossible to find the coordinates of the transition points using this criterion in the framework of the global Gibbs theory which describes the state of the entire macroscopic system. On the basis of the Ornstein-Zernike equation we formulate a local approach that analyzes the state of matter inside the correlation sphere of radius Rc \approx 10 Å. This approach is proved to be as rigorous as the Gibbs theory. In the context of the local approach we formulate a criterion that allows finding the transition points without calculating the chemical potential and the pressure of the second conjugate phase. In the second part of the review we consider second-order phase transitions (critical phenomena). The Kadanoff-Wilson theory of critical phenomena is analyzed, based on the global Gibbs approach. Again we use the Ornstein-Zernike equation to formulate a local theory of critical phenomena. With regard to experimentally established quantities this theory yields precisely the same results as the Kadanoff-Wilson theory; secondly, the local approach allows the prediction of many previously unknown details of critical phenomena, and thirdly, the local approach paves the way for constructing a unified theory of liquids that will describe the behavior of matter not only in the regular domain of the phase diagram, but also at the critical point and in its vicinity.

 Fulltext is available at IOP
PACS: 05.70.−a, 64.60.−i, 64.70.−p, 81.60.-s (all)
DOI: 10.1070/PU1999v042n06ABEH000543
URL: https://ufn.ru/en/articles/1999/6/b/
Citation: Martynov G A "The problem of phase transitions in statistical mechanics" Phys. Usp. 42 517–543 (1999)
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Оригинал: Мартынов Г А «Проблемы фазовых переходов в статистической механике» УФН 169 595–624 (1999); DOI: 10.3367/UFNr.0169.199906b.0595

References (55) Cited by (43) ↓ Similar articles (20)

1. Ning B-Yu, Gong L-Ch et al J. Phys.: Condens. Matter 33 115901 (2021)
2. Menon S V G Condensed Matter 6 29 (2021)
3. Ushcats M V, Bulavin L A Phys. Rev. E 101 (6) (2020)
4. Semyonov V I, Yu Ch A IOP Conf. Ser.: Mater. Sci. Eng. 643 012129 (2019)
5. Ushcats M V, Bulavin L A, Ushcats S Yu Phys. Rev. E 98 (4) (2018)
6. Ushcats M V, Ushcats S Yu et al Phys. Rev. E 98 (3) (2018)
7. Yukhnovskii I R Theor Math Phys 194 189 (2018)
8. Ushcats M V, Bulavin L A et al Phys. Rev. E 96 (6) (2017)
9. Schultz A J, Kofke D A Fluid Phase Equilibria 409 12 (2016)
10. Ushcats M V, Bulavin L A et al Journal Of Molecular Liquids 224 694 (2016)
11. Bobrov V B, Bobrov V B i dr Teoreticheskaya Matematicheskaya Fizika 183 120 (2015) [Bobrov V B, Trigger S A Theor Math Phys 183 553 (2015)]
12. Ushcats M V The Journal Of Chemical Physics 141 101103 (2014)
13. Ushcats M V Ushcats M V Ukr. J. Phys. 59 172 (2014)
14. Ushcats M V The Journal Of Chemical Physics 138 094309 (2013)
15. Bondarev V N, Bezverkhii P P, Kosenko S I Russ. J. Phys. Chem. 87 1838 (2013)
16. Ushcats M V Phys. Rev. E 87 (4) (2013)
17. Ushcats M V Phys. Rev. Lett. 109 (4) (2012)
18. Loktionov I K High Temp 50 708 (2012)
19. Bobrov V B, Trigger S A Physics Letters A 375 1716 (2011)
20. Myasnikova L P Encyclopedia of Polymer Science and Technology (2010)
21. Agrafonov Yu V, Petrushin V S et al Russ Phys J 52 1153 (2009)
22. Xu J, Bedrov D et al Phys. Rev. E 79 (1) (2009)
23. D’yakonov S G, Klinov A V, D’yakonov G S Russ. J. Phys. Chem. 83 875 (2009)
24. Martynov G A, Martynov G A Teor. Mat. Fiz. 156 454 (2008) [Martynov G A Theor Math Phys 156 1356 (2008)]
25. Martynov G A The Journal Of Chemical Physics 129 244509 (2008)
26. Bondarev V N Phys. Rev. E 77 (5) (2008)
27. Vasil’ev A N, Vasiliev A N Teor. Mat. Fiz. 153 124 (2007) [Vasil’ev A N Theor Math Phys 153 1458 (2007)]
28. Fortov V E, Gavrikov A V et al Physics Of Plasmas 14 040705 (2007)
29. Nesterov A S, Sanditov D S et al Glass Phys Chem 32 167 (2006)
30. Elfimova E A, Zubarev A Yu, Ivanov A O J. Exp. Theor. Phys. 103 917 (2006)
31. Martynov G A J Struct Chem 47 S99 (2006)
32. Nesterov A S, Sanditov D S et al Russ. J. Phys. Chem. 80 667 (2006)
33. Bondarev V N Phys. Rev. E 71 (5) (2005)
34. Martynov G A, Martynov G A Teor. Mat. Fiz. 134 325 (2003)
35. Sarkisov G N Uspekhi Fizicheskikh Nauk 172 647 (2002)
36. Kartashov Yu A, Popov I V Tech. Phys. Lett. 28 286 (2002)
37. Martynov G A Dokl. Phys. 46 396 (2001)
38. Malygin G A Uspekhi Fizicheskikh Nauk 171 187 (2001) [Malygin G A Phys.-Usp. 44 173 (2001)]
39. Murtazaev A K, Kamilov I K, Magomedov M A J. Exp. Theor. Phys. 93 1330 (2001)
40. Martynov G A Dokl. Phys. 46 310 (2001)
41. Sarkisov G The Journal Of Chemical Physics 114 9496 (2001)
42. Murtazaev A K, Kamilov I K, Khizriev K Sh Phys. Solid State 43 685 (2001)
43. Martynov G A, Martynov G A Teor. Mat. Fiz. 123 500 (2000) [Martynov G A Theor Math Phys 123 833 (2000)]

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