Advertisement

Universality of Critical Phenomena in Classical Fluids

  • J. V. Sengers

Abstract

To characterize the asymptotic behavior of the physical properties of systems near a critical point, critical-point phase transitions are grouped into universality classes as first suggested by Kadanoff (1971). Systems with critical-point phase transitions assigned to the same universality class have identical critical exponents and identical scaling functions. Universality classes are distinguished by such general features as the dimensionality of the system, the number of components of the order parameter and whether the intermolecular forces are short- or long-range. Universality classes can be further distinguished with respect to the critical behavior of static and dynamic properties.

Keywords

Critical Temperature Ising Model Critical Exponent Amplitude Ratio Critical Phenomenon 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aharony, A., and G. Ahlers (1980), Phys. Rev. Lett. 44, 782.ADSCrossRefGoogle Scholar
  2. Aharony, A. and P. C. Hohenberg (1976), Phys. Rev. B 13 3081.ADSGoogle Scholar
  3. Baker, G. A. (1977), Phys. Rev. B 15 1552.ADSGoogle Scholar
  4. Baker, G. A. and J. M. Kincaid (1980), J. Stat. Phys. (in press).Google Scholar
  5. Baker, G. A., B. G, Nickel, M. S. Green and D. I. Meiron (1976), Phys. Rev. Lett. 36, 1351.ADSCrossRefGoogle Scholar
  6. Baker, G. A., B. G. Nickel and D. I. Meiron (1978), Phys. Rev. B 17, 1365.ADSCrossRefGoogle Scholar
  7. Bale, H. D. , J. S. Lin, D. A. Dolejsi, J. L. Casteel, O. A. Pringle and P. W. Schmidt (1977), Phys. Rev. A 15, 2513.ADSCrossRefGoogle Scholar
  8. Balfour, F. W. , J. V. Sengers, M. R. Moldover and J. M. H. Levelt Sengers (1977), in Proceedings 7th Symposium on Thermophysical Properties, A. Cezairliyan, ed. (American Society of Mechanical Engineers, New York), p. 786.Google Scholar
  9. Balfour, F. W. , J. V. Sengers, M. R. Moldover and J. M. H. Levelt Sengers (1978), Phys. Lett. 65A, 223.ADSGoogle Scholar
  10. Balfour, F. W., J. V. Sengers, and J. M. H. Levelt Sengers (1980), in Water and Steam: Their Properties and Current Applications, J. Straub and K. Scheffler, eds. (Pergamon Press, Oxford and New York), p. 128.Google Scholar
  11. Balzarini, D. A. (1974), Canad. J. Phys. 52, 499.ADSGoogle Scholar
  12. Balzarini, D. A. and K. Ohrn (1972), Phys Rev. Lett. 29, 840.ADSCrossRefGoogle Scholar
  13. Basu, R. S., J. V. Sengers and J. T. R. Watson (1980), Intern. J. Thermophys. 1, 33.ADSCrossRefGoogle Scholar
  14. Bervillier, C. and C. Godrèche (1980), Phys. Rev. B 21, 5427.MathSciNetADSCrossRefGoogle Scholar
  15. Beysens, D. (1979), J. Chem. Phys. 71, 2557.ADSCrossRefGoogle Scholar
  16. Beysens, D. and A. Bourgou (1979), Phys. Rev. A 19 2407.ADSCrossRefGoogle Scholar
  17. Beysens, D., R. Tufeu and Y. Garrabos (1979), J. Physique 40, L-623.Google Scholar
  18. Bhattacharjee, J. K. and R. A. Ferrell (1980), Phys, Rev. A. (in press).Google Scholar
  19. Bloemen, E., J. Thoen and W. Van Dael (1980), J. Chem. Phys. (in press).Google Scholar
  20. Bray, A. J. (1976), Phys. Rev. Lett. 36, 285; Phys. Rev. B 14, 1248.ADSCrossRefGoogle Scholar
  21. Burstyn, H. C. (1979), “An examination of the structure factor, near the consolute point, in the binary liquid 3-methylpentane+ nitroethane”, thesis (Department of Physics and Astronomy, University of Maryland, College Park, MD).Google Scholar
  22. Burstyn, H. C., R. F. Chang and J. V. Sengers (1980), Phys. Rev. Lett. 44, 410.ADSCrossRefGoogle Scholar
  23. Burstyn, H. C. and J. V. Sengers (1980), Phys. Rev. Lett. 45, 259.ADSCrossRefGoogle Scholar
  24. Burstyn, H. C., J. V. Sengers and P. Esfandiari (1980), Phys. Rev. A 22, 282.ADSCrossRefGoogle Scholar
  25. Calmettes, P. (1977), Phys. Rev. Lett. 39, 1151.ADSCrossRefGoogle Scholar
  26. Camp, W. J., D. M. Saul, J. P. Van Dyke and M. Wortis (1976), Phys. Rev. B 14, 3990.ADSCrossRefGoogle Scholar
  27. Cannell, D. S. (1975), Phys. Rev. A 12, 225.ADSCrossRefGoogle Scholar
  28. Cannell, D. S. and H. Güttinger (1980), private communication.Google Scholar
  29. Chang, M. C. and A. Houghton (1980), Phys. Rev. Lett. 44, 785; Phys. Rev. B 21, 1881.ADSCrossRefGoogle Scholar
  30. Chang, R. F., H. Burstyn, J. V. Sengers and A. J. Bray (1976), Phys. Rev. Lett. 37, 1481.ADSCrossRefGoogle Scholar
  31. Chang, R. F., H. Burstyn and J. V. Sengers (1979), Phys. Rev. A 19, 866.ADSCrossRefGoogle Scholar
  32. Chang, R. F., P. H. Keyes, J. V. Sengers and C. O. Alley (1971), Phys. Rev. Lett. 27, 1706.ADSCrossRefGoogle Scholar
  33. Chang, R. F., P. H. Keyes, J. V. Sengers and C. O. Alley (1972), Ber. Bunsenges. physik. Chemie 76, 260.Google Scholar
  34. Chen, S. H. , C. C. Lai and J. Rouch (1978), J. Chem. Phys. 68, 1994.ADSCrossRefGoogle Scholar
  35. Chu, B. (1972), J. Stat. Phys. 6, 173; Ber. Bunsenges. physik. Chemie 76, 202.ADSCrossRefGoogle Scholar
  36. Chu, B. and F. L. Lin (1974), J. Chem. Phys. 61, 5132.ADSCrossRefGoogle Scholar
  37. Domb, C. (1974), in Phase Transitions and Critical Phenomena, Vol 3, C. Domb and M. S. Green, eds. (Academic Press, New York), Ch. 6.Google Scholar
  38. Estler, W. T., R. Hocken, T. Charlton and L. R. Wilcox (1975), Phys. Rev. A 12, 2118.ADSCrossRefGoogle Scholar
  39. Ferrell, R. A. (1970), Phys. Rev. Lett. 24, 1169.ADSCrossRefGoogle Scholar
  40. Ferrell, R. A., N. Menyhárd. H. Schmidt, F. Schwabl and P. Szépfalusy (1968), Ann. Phys, (N.Y.) 47, 565.ADSCrossRefGoogle Scholar
  41. Ferrell, R. A. and D. J. Scalapino (1975), Phys. Rev. Lett. 34, 200.ADSCrossRefGoogle Scholar
  42. Fisher, M. E. (1964), J. Math. Phys. 5, 944.ADSCrossRefGoogle Scholar
  43. Fisher, M. E. (1967), Reports Progr. Phys. 30 (II), 615.ADSCrossRefGoogle Scholar
  44. Fisher, M. E. and R. J. Burford (1974), Phys. Rev. B 10, 2818.ADSCrossRefGoogle Scholar
  45. Garisto, F. and R. Kapral (1976), Phys. Rev. A 14, 884.ADSCrossRefGoogle Scholar
  46. Green, M. S., M. J. Cooper and J. M. H. Levelt Sengers (1971). Phys. Rev. Lett. 26, 492, 941.ADSCrossRefGoogle Scholar
  47. Greer, S. C. (1976), Phys. Rev. A 14, 1770.ADSCrossRefGoogle Scholar
  48. Greer, S. C. (1978), Acc. Chem. Res. 11, 427.CrossRefGoogle Scholar
  49. Greer, S. C. and R. Hocken (1975) , J. Chem. Phys. 63, 5067.ADSCrossRefGoogle Scholar
  50. Griffiths, R. B. and J. C. Wheeler (1970), Phys. Rev. A 2, 1047.ADSCrossRefGoogle Scholar
  51. Gürmen, E., M. Chandrasekhar, P. E. Chumbley, H. D. Bale, D. A. Dolejsi, J. S. Lin and P. W. Schmidt (1980), Phys. Rev. A 22, 170.ADSCrossRefGoogle Scholar
  52. Güttinger, H. and D. S. Cannell (1980), Phys. Rev. A 22, 285.ADSCrossRefGoogle Scholar
  53. Gunton, J. D. (1979), in Dynamical Critical Phenomena and Related Topics, C. P. Enz, ed. (Springer-Verlag, Berlin, Heidelberg, New York), p. 1.CrossRefGoogle Scholar
  54. Halperin, B. I. and P. C. Hohenberg (1969), Phys. Rev. 177, 952.ADSCrossRefGoogle Scholar
  55. Hankey, A. and H. E. Stanley (1972), Phys. Rev. B 6, 3515.ADSCrossRefGoogle Scholar
  56. Harker, G. G. and R. L. Schmidt (1977), J. Chem. Phys. 67, 332.ADSCrossRefGoogle Scholar
  57. Hastings, J. R. , J. M. H. Levelt Sengers and F. W. Balfour (1980), J. Chem. Thermod. (in press).Google Scholar
  58. Hayes, C. E. and H. Y. Carr (1977), Phys. Rev. Lett. 24, 1558.ADSCrossRefGoogle Scholar
  59. Hocken, R. and M. R. Moldover (1976), Phys. Rev. Lett. 37 29.ADSCrossRefGoogle Scholar
  60. Hohenberg, P. C. and M. Barmatz (1972), Phys. Rev. A 6, 289.ADSCrossRefGoogle Scholar
  61. Hohenberg, P. C., A. Aharony, B. I. Halperin and E. D. Siggia (1976), Phys. Rev. B 13, 2986.ADSCrossRefGoogle Scholar
  62. Hohenberg, P. C. and B. I. Halperin (1977), Rev. Mod. Phys. 49, 435.ADSCrossRefGoogle Scholar
  63. Jacobs, D. T., D. J. Anthony, R. C. Mockler and W. J. O’Sullivan (1977), Chem. Phys. 20, 219.CrossRefGoogle Scholar
  64. Kadanoff, L. P. (1971), in Critical Phenomena, Proc. Intern. School of Physics, “Enrico Fermi”, Course LI, M. S. Green, ed. (Academic Press, New York), p. 100.Google Scholar
  65. Kawasaki, K. (1970), Ann. Phys. (N.Y.) 61, 1.ADSCrossRefGoogle Scholar
  66. Klein, H. and D. Woermann (1976), J. Chem. Phys. 64, 5316.ADSCrossRefGoogle Scholar
  67. Lee, S. P. (1978), Chem. Phys. Lett. 57, 611.ADSCrossRefGoogle Scholar
  68. Lee, T. and C. N. Yang (1952), Phys. Rev. 87, 410.MathSciNetADSMATHCrossRefGoogle Scholar
  69. Le Guillou, J. C. and J. Zinn-Justin (1977), Phys. Rev. Lett. 39, 95.ADSCrossRefGoogle Scholar
  70. Le Guillou, J. C. and J. Zinn-Justin (1980), Phys. Rev. B 21, 3976.MathSciNetADSCrossRefGoogle Scholar
  71. Leung, S. S. and R. B. Griffiths (1973), Phys. Rev. A 8, 2670.ADSCrossRefGoogle Scholar
  72. Levelt Sengers, J. M. H. (1974), Physica 73, 73.ADSCrossRefGoogle Scholar
  73. Levelt Sengers, J. M. H. (1975), in Experimental Thermodynamics Vol. II, B. Le Neindre and B. Vodar, eds. (Butterworth, London) p. 657.Google Scholar
  74. Levelt Sengers, J. M. H. , W. L. Greer and J. V. Sengers (1976), J. Phys. Chem. Ref. Data 5, 1.ADSCrossRefGoogle Scholar
  75. Levelt Sengers, J. M. H. and J. V. Sengers (1975), Phys. Rev. A 12, 2622.ADSCrossRefGoogle Scholar
  76. Levelt Sengers, J. M. H. and J. V. Sengers (1980), in Perspectives in Statistical Physics, H. J. Raveché, ed. (North-Holland Publ. Comp, Amsterdam, in press).Google Scholar
  77. Ley-Koo, M. (1976), “Consequences of the renormalization group for the thermodynamics of fluids near the critical point”, thesis (Department of Physics, Temple University, Philadelphia, PA).Google Scholar
  78. Ley-Koo, M. and M. S. Green (1977), Phys. Rev. A 16, 2483.ADSCrossRefGoogle Scholar
  79. Lin, J. S. and P. W. Schmidt (1974), Phys. Rev. A 10, 2290.ADSCrossRefGoogle Scholar
  80. Lipa, J. A., C. Edwards and M. S. Buckingham (1977), Phys. Rev. A 15, 778.ADSCrossRefGoogle Scholar
  81. Lunacek, J. H. and D. S. Cannell (1971), Phys. Rev. Lett. 27, 841.ADSCrossRefGoogle Scholar
  82. Mazenko, G. (1978), in Correlation Functions and Quasiparticle Interactions, J. W. Halley, ed. (Plenum Publ. Corp., New York) p. 1.Google Scholar
  83. McKenzie, S. (1979), J. Phys. A 12, L185.ADSCrossRefGoogle Scholar
  84. Mermin, N. D. (1971), Phys. Rev. Lett. 26, 957.ADSCrossRefGoogle Scholar
  85. Mermin, N. D. and J. J. Rehr (1971), Phys. Rev. Lett. 26, 1155.ADSCrossRefGoogle Scholar
  86. Mistura, L. (1979), Nuovo Cim. 52B, 277.ADSCrossRefGoogle Scholar
  87. Moldover, M. R. (1969), Phys. Rev. 182, 342.ADSCrossRefGoogle Scholar
  88. Moldover, M. R. , J. V. Sengers, R. W. Gammon and R. J. Hocken (1979), Rev. Mod. Phys. 51, 79.ADSCrossRefGoogle Scholar
  89. Moore, M. A. , D. Jasnow and M. Wortis (1969), Phys. Rev. Lett. 22, 940.ADSCrossRefGoogle Scholar
  90. Morrison, G. and C. M. Knobler (1976), J. Chem. Phys. 65, 5507.ADSCrossRefGoogle Scholar
  91. Nagarajan, N., A. Kumar, E. S. R. Gopal and S. C. Greer (1980), J. Phys. Chem. 84, 2883.CrossRefGoogle Scholar
  92. Nakata, M. , T. Dobashi, N. Kuwara, M. Kaneko and B. Chu (1978), Phys. Rev. A 18, 2683.ADSCrossRefGoogle Scholar
  93. Nickel, B. G. and B. Sharpe (1979), J. Phys. A 12, 1819.ADSCrossRefGoogle Scholar
  94. Nicoll, J. F. (1980), Phys. Rev. A (in press).Google Scholar
  95. Nicoll, J. F. and R. K. P. Zia (1980), Phys. Rev. B (in press).Google Scholar
  96. Ohta, T. (1977), J. Phys. C 10, 791.ADSCrossRefGoogle Scholar
  97. Oitmaa, J. and J. Ho-Ting-Hun (1979), J. Phys. A 12, L281.ADSCrossRefGoogle Scholar
  98. Oxtoby, D. W. and W. M. Gelbart (1974), J. Chem. Phys. 61, 2957.ADSCrossRefGoogle Scholar
  99. Patashinkii, A. Z. and V. I. Pokrovskii (1979), Fluctuation Theory of Phase Transitions (Pergamon Press, New York).Google Scholar
  100. Pelger, M., H. Klein and D. Woermann (1977), J. Chem. Phys. 67, 5362.ADSCrossRefGoogle Scholar
  101. Pfeuty, P. and G. Toulouse (1977), Introduction to the Renormalization Group and to Critical Phenomena (Wiley, New York).Google Scholar
  102. Pittman, C., T. Doiron and H. Meyer (1979), Phys. Rev. B 20, 3678.ADSCrossRefGoogle Scholar
  103. Rehr, J. J. (1979), J. Phys. A 12, L179.ADSCrossRefGoogle Scholar
  104. Rehr, J. J. and N. D. Mermin (1973), Phys. Rev. A 8, 472.ADSCrossRefGoogle Scholar
  105. Rowlinson, J. S. (1969), Nature 224, 541.ADSCrossRefGoogle Scholar
  106. Saam, W. F. (1970), Phys. Rev. A 2, 1461.ADSCrossRefGoogle Scholar
  107. Scheibner, B. A., C. M. Sorensen, D. T. Jacobs, R. C. Mockler and W. J. O’Sullivan (1978), Chem. Phys. 31, 209.CrossRefGoogle Scholar
  108. Schmidt, H. H. (1971), J. Chem. Phys. 54, 3610.ADSCrossRefGoogle Scholar
  109. Schneider, R., L. Belkoura, J. Schelten, D. Woermann and B. Chu (1980), Phys. Rev. A (in press).Google Scholar
  110. Scott, R. L. (1978), in Chemical Thermodynamics, Vol. 2, Specialist Periodical Report, M. L. McGlashnan, ed. (Chemical Society, London), p. 238.Google Scholar
  111. Sengers, J. V. (1972), Ber. Bunsenges. physik. Chemie 76, 234.Google Scholar
  112. Sengers, J. V., D. Bedeaux, P. Mazur and S. C. Greer (1980), Physica A (in press).Google Scholar
  113. Sengers, J. V. and P. H. Keyes (1971), Phys. Rev. Lett. 26, 70.ADSCrossRefGoogle Scholar
  114. Sengers, J. V. and J. M. H. Levelt Sengers (1978), in Progress in Liquid Physics, C. A. Croxton, ed. (Wiley, New York, 1978), Ch. 4.Google Scholar
  115. Sengers, J. V. and M. R. Moldover (1978a), in Cospar: Space Research, Vol. XVIII, M. J. Rycroft and A. C. Strickland, eds. (Pergamon Press, N.Y.), p. 495; Z. Flugwiss. Weltraumforsch. 2, 371.Google Scholar
  116. Sengers, J. V. and M. R. Moldover (1978b), Phys. Lett. 66A, 44.ADSGoogle Scholar
  117. Sheludyak, Yu. E. and V. A. Rabinovich (1979), High Temp. 17, 40.Google Scholar
  118. Siggia, E. D., B. I. Halperin, and P. C. Hohenberg (1976), Phys. Rev. B 13, 2110.ADSCrossRefGoogle Scholar
  119. Sorensen, C. M. , R. C. Mockley and W. J. O’Sullivan (1978), Phys. Rev. Lett. 40, 777.ADSCrossRefGoogle Scholar
  120. Stauffer, D., M. Ferer and M. Wortis (1972), Phys. Rev. Lett. 29, 345.ADSCrossRefGoogle Scholar
  121. Stein, A. and G. F. Allen (1974), J. Phys. Chem. Ref. Data 2, 443.ADSCrossRefGoogle Scholar
  122. Swinney, H. L. and D. L. Henry (1973), Phys. Rev. A 8, 2586.ADSCrossRefGoogle Scholar
  123. Thijsse, B. J. (1980), to be published.Google Scholar
  124. Thoen, J. , E. Bloemen and W. Van Dael (1978), J. Chem. Phys. 68, 735.ADSCrossRefGoogle Scholar
  125. Tsai, B. C. and D. McIntyre (1974), J. Chem. Phys. 60, 937.ADSCrossRefGoogle Scholar
  126. Vause, C. and J. Sak (1980), Phys. Lett. 77A, 191; Phys. Rev. A 21, 2099.MathSciNetADSGoogle Scholar
  127. Wallace, D. J. and R. K. P. Zia (1974), J. Phys. C 7, 3480.ADSCrossRefGoogle Scholar
  128. Warkulwiz, V. P., B. Mozer and M. S. Green (1974), Phys. Rev. Lett. 32, 1410.ADSCrossRefGoogle Scholar
  129. Wegner, F. J. (1972a), Phys. Rev. B 5, 4529.ADSCrossRefGoogle Scholar
  130. Wegner, F. J. (1972b), Phys. Rev. B 6 1891.ADSGoogle Scholar
  131. Wegner, F. J. (1975), J. Phys. A 8, 710.MathSciNetADSCrossRefGoogle Scholar
  132. Wheeler, J. C. (1977), Ann. Rev. Phys. Chem. 28, 411.ADSCrossRefGoogle Scholar
  133. Widom, B. (1965), J. Chem. Phys. 43, 3898.ADSCrossRefGoogle Scholar
  134. Widom, B. and J. S. Rowlinson (1970), J. Chem. Phys. 52, 1670.ADSCrossRefGoogle Scholar
  135. Wilcox, L. R. and D. Balzarini (1968), J. Chem. Phys. 48, 753.ADSCrossRefGoogle Scholar
  136. Wilson, K. G. and J. Kogut (1974), Physics Reports 12C, 75.ADSCrossRefGoogle Scholar
  137. Zinn-Justin, J. (1979), J. Physique 40, 63.MathSciNetCrossRefGoogle Scholar
  138. Zollweg, J. A. and G. W. Mulholland (1972), J. Chem. Phys. 57, 1021.ADSCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1982

Authors and Affiliations

  • J. V. Sengers
    • 1
  1. 1.Institute for Physical Science and TechnologyUniversity of MarylandCollege ParkUSA

Personalised recommendations