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
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. G.N. Sarkisov “Approximate equations of the theory of liquids in the statistical thermodynamics of classical liquid systems42 545–561 (1999)
  2. I.K. Kamilov, A.K. Murtazaev, Kh.K. Aliev “Monte Carlo studies of phase transitions and critical phenomena42 689–709 (1999)
  3. G.N. Sarkisov “Molecular distribution functions of stable, metastable and amorphous classical models45 597–617 (2002)
  4. A.A. Likal’ter “Critical points of condensation in Coulomb systems43 777–797 (2000)
  5. L.I. Klushin, A.M. Skvortsov, A.A. Gorbunov “An exactly solvable model for first- and second-order transitions41 639–649 (1998)
  6. A.V. Bushman, V.E. Fortov “Model equations of state26 465–496 (1983)
  7. R.S. Berry, B.M. Smirnov “Phase transitions and adjacent phenomena in simple atomic systems48 345–388 (2005)
  8. A.Yu. Grosberg “Disordered polymers40 125–158 (1997)
  9. V.F. Gantmakher, V.T. Dolgopolov “Localized-delocalized electron quantum phase transitions51 3–22 (2008)
  10. A.I. Olemskoi “Theory of stochastic systems with singular multiplicative noise41 269–301 (1998)
  11. V.S. Vikhrenko “Theory of depolarized molecular light scattering17 558–576 (1975)
  12. A.I. Alekseev “The application of the methods of quantum field theory in statistical physics4 23–50 (1961)
  13. A.L. Roitburd “The theory of the formation of a heterophase structure in phase transformations in solids17 326–344 (1974)
  14. I.S. Lyubutin, A.G. Gavriliuk “Research on phase transformations in 3d-metal oxides at high and ultrahigh pressure: state of the art52 989–1017 (2009)
  15. M.A. Anisimov, E.E. Gorodetskii, V.M. Zaprudskii “Phase transitions with coupled order parameters24 57–75 (1981)
  16. V.P. Skripov, A.V. Skripov “Spinodal decomposition (phase transitions via unstable states)22 389–410 (1979)
  17. G.A. Martynov “Statistical theory of electrolyte solutions of intermediate concentrations10 171–187 (1967)
  18. V.G. Boiko, Kh.I. Mogel’ et alFeatures of metastable states in liquid-vapor phase transitions34 (2) 141–159 (1991)
  19. S.M. Stishov “Quantum phase transitions47 789–795 (2004)
  20. L.I. Manevich, A.V. Savin et alSolitons in nondegenerate bistable systems37 859–879 (1994)

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