Phase transitions

  • Zevi W. Salsburg
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 7)


Phase Transition Partition Function Thermodynamic Limit Order Phase Transition Helmholtz Free Energy 
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  1. [1]
    L. D. LANDAU AND E. M. LIFSHITZ: Statistical Physics (2nd edition), Addison-Wesley Pub. Co., Reading (1969).Google Scholar
  2. [2]
    P. EHRENFEST: Commun. Kamerlingh Omnes Lab. Univ. Leiden Suppl. 75b (1933).Google Scholar
  3. [3]
    J. GRINDLAY: Can. J. Phys. 46, 2253 (1968).Google Scholar
  4. [4]
    J. L. BIRMAN: “Symmetry Changes, Phase Transitions and Ferroelectricity” in Ferroelectricity (Proceedings of a Symposium-1966) pp. 20–61, edited by Weller, Elsevier Pub. Co., Inc., N. Y. (1967). In this paper the reader will find a detailed analysis of Landau's theory of second order phase transitions.Google Scholar
  5. [5]
    L. TISZA: “On the General Theory of Phase Transitions” in Phase Transformations in Solids, pp. 1–37, edited by Smoluchowski, Mayer and Weyl, J. Wiley, New York (1951) See also V. Dvorak and V. Janovec, Bull. Acad. Sci. USSR Phys. Ser. 33, 165 (1969).Google Scholar
  6. [6]
    L. ONSAGER: Phys. Rev. 65, 117 (1966).Google Scholar
  7. [7]
    J. C. WEELER AND R. B. GRIFFITHS:Phys. Rev. 170, 249 (1968)Google Scholar
  8. [8]
    R. BROUT: Phase Transitions, W. A. Benjamin, New York (1965)Google Scholar
  9. [9]
    see e.g. T. L. HILL: Statistical Mechanics, McGraw-Hill New York (1956) or 15 below.Google Scholar
  10. [10]
    see in Fundamental Problems in Statistical Mechanics Pt. 2 compiled by E. G. D. Cohen, North Holland, Amsterdam 1968: N. M. HUGENHOLTZ: “Quantum Mechanics of Infinitely Large Systems”, pp. 197–227; and D. RUELLE: “On the Gibbs Phase Rule”, pp. 113-39.Google Scholar
  11. [11]
    D. RUELLE: Statistical Mechanics, W. A. Benjamin, New York (1969).Google Scholar
  12. [12]
    see e.g. P. A. EGELSTAFF: An Introduction to the Liquid State, Academic Press, London and New York (1967).Google Scholar
  13. [13]
    P. W. KASTELEYN: J. Math. Phys. 4, 287 (1963).Google Scholar
  14. [14]
    C. N. YANG AND T. D. LEE: Phys. Rev. 87, 404 (1952).Google Scholar
  15. [14a]
    T. D. LEE AND C. N. YANG: Phys. Rev. 87, 410 (1952).Google Scholar
  16. [15]
    A. MUNSTER: Statistical Thermodynamics, vol. I., SpringerVerlag, New York (1968).Google Scholar
  17. [16]
    M. Suzuki: J. Math. Phys. 9, 2064 (1968). In this paper the theorem of Yang and Lee has been extended to the ferromagnetic Ising model with arbitrarily mixed spin values of Sj = 1/2, 1 and 3/2 including the case of equal spin values as a speical one.Google Scholar
  18. [17]
    T. ASANO: Phys. Rev. Letters 24, 1409 (1970). In this paper Yang and Lee's results are extended to the anisotropic Heisenberg ferromagnet. See for a lattice gas O. J. HEILMAN: J. Math. Phys. 11, 2701 (1970). For the dilute Ising model, the anisotropic planar model, the anisotropic classical Heisenberg model and the monomerdimer model, see H. KUNZ 32A, 311 (1970)-Phys. Letters.Google Scholar
  19. [18]
    P. C. HEMMER, E. H. HAUGUE AND J. O. AASEN: J. Math. Phys. 7, 35 (1966).Google Scholar
  20. [19]
    B. J. ALDER AND W. G. HOOVER: “Numerical Statistical Mechanics”, in ref. G-4 above, pp. 81–113.Google Scholar
  21. [20]
    W. W. WOOD: “Monte Carlo Studies of Simple Liquid Models” in ref. G-4 above, pp. 116–230.Google Scholar
  22. [21]
    N. OGITA et. al.: J. Phys. Soc. (Japan) 26, suppl., 145 (1969). The authors have studied 2-D Ising model type systems on the computer and obtained good agreement with the exact results of Onsager.Google Scholar
  23. [22]
    M. KAC: “Toward a Unified View on Mathematical Theories of Phase Transitions” in reference 10 above, pp. 71–105.Google Scholar
  24. [23]
    F. H. REE AND D. A. CHESNUT: J. Chem. Phys. 45, 3983 (1966)Google Scholar
  25. [24]
    A. BELLEMANS AND R. K. NIGAM: Phys. Rev. Letters 16, 1038 (1966).Google Scholar
  26. [25]
    M. KAC, G. E. UHLENBECK AND P. C. HEMMER: J. Math. Phys. 4, 216 (1963). See also ref. G.4 above.Google Scholar
  27. [26]
    J. LEBOWITZ AND O. PENROSE: J. Math. Phys. 7, 98 (1966).Google Scholar
  28. [27]
    P. W. KASTELEYN: “Phase Transitions”, in reference 10 above pp. 30–70.Google Scholar
  29. [28]
    E. LIEB: “The Solution of the Rys F Model”, Phys. Rev. Letters 18, 1046 (1967) and “The Solution of the KDP Model”, Phys. Rev. Letters 79, 108 (1967); see also Phys. Rev. 162, 162 (1967).Google Scholar
  30. [29]
    R. ZWANZIG AND J. I. LAURITZEN, JR.: J. Chem. Phys. 48, 3351 (1968).Google Scholar
  31. [30]
    See the review article by J. L. LEBOWITZ: Ann. Rev. Phys. Chem. 19, 389 (1968).Google Scholar
  32. [31]
    N. D. MERMIN: J. Math. Phys. 8, 1061 (1967). For the impossibility of crystal ordering in one and two-dimensional systems see B. I. SADOVNIKOV And E. M. SOROKINA: Sov. Phys. Dokl. 14, 968 (1970); Indian J. Pure Appl. Phys. 8, 61 (1970); E. M. SOROKINA: Ibid. 8, 64 (1970), Sov. Phys. Dokl. 15, 23 (1970).Google Scholar
  33. [32]
    H. FALK: Physica 29, 1114 (1963).Google Scholar
  34. [33]
    A. ISIHARA: J. Phys. A. (Proc. Phys. Soc.) 1, 539 (1968).Google Scholar
  35. [34]
    R. E. PEIERLS: Helv. Phys. Acta 7, suppl. 2, 81 (1934).Google Scholar
  36. [34a]
    Ann. Inst. H. Poincaré 5, 177 (1935).Google Scholar
  37. [35]
    P. W. BRIDGMAN: See e.g. Rev. Mod. Phys. 18, 1 (1948), where account of earlier work is given.Google Scholar
  38. [36]
    F. W. DE WETTE, R. E. ALLEN AND D. S. HUGHES: Phys. Lett. 29a, 548 (1969).Google Scholar
  39. [37]
    J. P. HANSEN AND L. VERLET: Phys. Rev. 184, 151 (1969).Google Scholar
  40. [38]
    W. G. HOOVER AND F. H. REE: J. Chem. Phys. 47 (1967), J. Chem. Phys. 49 (1968).Google Scholar
  41. [39]
    G. EMCH, H. J. KNOPS AND E. J. VERBOVEN: J. Math. Phys. 11 1655 (1970).Google Scholar
  42. [40]
    H. J. MIKESKA AND H. SCHMIDT: J. Low. Temp. Phys. 2, 371 (1970)Google Scholar

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© Springer Verlag 1971

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  • Zevi W. Salsburg

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