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.
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References
Aharony, A., and G. Ahlers (1980), Phys. Rev. Lett. 44, 782.
Aharony, A. and P. C. Hohenberg (1976), Phys. Rev. B 13 3081.
Baker, G. A. (1977), Phys. Rev. B 15 1552.
Baker, G. A. and J. M. Kincaid (1980), J. Stat. Phys. (in press).
Baker, G. A., B. G, Nickel, M. S. Green and D. I. Meiron (1976), Phys. Rev. Lett. 36, 1351.
Baker, G. A., B. G. Nickel and D. I. Meiron (1978), Phys. Rev. B 17, 1365.
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.
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.
Balfour, F. W. , J. V. Sengers, M. R. Moldover and J. M. H. Levelt Sengers (1978), Phys. Lett. 65A, 223.
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.
Balzarini, D. A. (1974), Canad. J. Phys. 52, 499.
Balzarini, D. A. and K. Ohrn (1972), Phys Rev. Lett. 29, 840.
Basu, R. S., J. V. Sengers and J. T. R. Watson (1980), Intern. J. Thermophys. 1, 33.
Bervillier, C. and C. Godrèche (1980), Phys. Rev. B 21, 5427.
Beysens, D. (1979), J. Chem. Phys. 71, 2557.
Beysens, D. and A. Bourgou (1979), Phys. Rev. A 19 2407.
Beysens, D., R. Tufeu and Y. Garrabos (1979), J. Physique 40, L-623.
Bhattacharjee, J. K. and R. A. Ferrell (1980), Phys, Rev. A. (in press).
Bloemen, E., J. Thoen and W. Van Dael (1980), J. Chem. Phys. (in press).
Bray, A. J. (1976), Phys. Rev. Lett. 36, 285; Phys. Rev. B 14, 1248.
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).
Burstyn, H. C., R. F. Chang and J. V. Sengers (1980), Phys. Rev. Lett. 44, 410.
Burstyn, H. C. and J. V. Sengers (1980), Phys. Rev. Lett. 45, 259.
Burstyn, H. C., J. V. Sengers and P. Esfandiari (1980), Phys. Rev. A 22, 282.
Calmettes, P. (1977), Phys. Rev. Lett. 39, 1151.
Camp, W. J., D. M. Saul, J. P. Van Dyke and M. Wortis (1976), Phys. Rev. B 14, 3990.
Cannell, D. S. (1975), Phys. Rev. A 12, 225.
Cannell, D. S. and H. Güttinger (1980), private communication.
Chang, M. C. and A. Houghton (1980), Phys. Rev. Lett. 44, 785; Phys. Rev. B 21, 1881.
Chang, R. F., H. Burstyn, J. V. Sengers and A. J. Bray (1976), Phys. Rev. Lett. 37, 1481.
Chang, R. F., H. Burstyn and J. V. Sengers (1979), Phys. Rev. A 19, 866.
Chang, R. F., P. H. Keyes, J. V. Sengers and C. O. Alley (1971), Phys. Rev. Lett. 27, 1706.
Chang, R. F., P. H. Keyes, J. V. Sengers and C. O. Alley (1972), Ber. Bunsenges. physik. Chemie 76, 260.
Chen, S. H. , C. C. Lai and J. Rouch (1978), J. Chem. Phys. 68, 1994.
Chu, B. (1972), J. Stat. Phys. 6, 173; Ber. Bunsenges. physik. Chemie 76, 202.
Chu, B. and F. L. Lin (1974), J. Chem. Phys. 61, 5132.
Domb, C. (1974), in Phase Transitions and Critical Phenomena, Vol 3, C. Domb and M. S. Green, eds. (Academic Press, New York), Ch. 6.
Estler, W. T., R. Hocken, T. Charlton and L. R. Wilcox (1975), Phys. Rev. A 12, 2118.
Ferrell, R. A. (1970), Phys. Rev. Lett. 24, 1169.
Ferrell, R. A., N. Menyhárd. H. Schmidt, F. Schwabl and P. Szépfalusy (1968), Ann. Phys, (N.Y.) 47, 565.
Ferrell, R. A. and D. J. Scalapino (1975), Phys. Rev. Lett. 34, 200.
Fisher, M. E. (1964), J. Math. Phys. 5, 944.
Fisher, M. E. (1967), Reports Progr. Phys. 30 (II), 615.
Fisher, M. E. and R. J. Burford (1974), Phys. Rev. B 10, 2818.
Garisto, F. and R. Kapral (1976), Phys. Rev. A 14, 884.
Green, M. S., M. J. Cooper and J. M. H. Levelt Sengers (1971). Phys. Rev. Lett. 26, 492, 941.
Greer, S. C. (1976), Phys. Rev. A 14, 1770.
Greer, S. C. (1978), Acc. Chem. Res. 11, 427.
Greer, S. C. and R. Hocken (1975) , J. Chem. Phys. 63, 5067.
Griffiths, R. B. and J. C. Wheeler (1970), Phys. Rev. A 2, 1047.
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.
Güttinger, H. and D. S. Cannell (1980), Phys. Rev. A 22, 285.
Gunton, J. D. (1979), in Dynamical Critical Phenomena and Related Topics, C. P. Enz, ed. (Springer-Verlag, Berlin, Heidelberg, New York), p. 1.
Halperin, B. I. and P. C. Hohenberg (1969), Phys. Rev. 177, 952.
Hankey, A. and H. E. Stanley (1972), Phys. Rev. B 6, 3515.
Harker, G. G. and R. L. Schmidt (1977), J. Chem. Phys. 67, 332.
Hastings, J. R. , J. M. H. Levelt Sengers and F. W. Balfour (1980), J. Chem. Thermod. (in press).
Hayes, C. E. and H. Y. Carr (1977), Phys. Rev. Lett. 24, 1558.
Hocken, R. and M. R. Moldover (1976), Phys. Rev. Lett. 37 29.
Hohenberg, P. C. and M. Barmatz (1972), Phys. Rev. A 6, 289.
Hohenberg, P. C., A. Aharony, B. I. Halperin and E. D. Siggia (1976), Phys. Rev. B 13, 2986.
Hohenberg, P. C. and B. I. Halperin (1977), Rev. Mod. Phys. 49, 435.
Jacobs, D. T., D. J. Anthony, R. C. Mockler and W. J. O’Sullivan (1977), Chem. Phys. 20, 219.
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.
Kawasaki, K. (1970), Ann. Phys. (N.Y.) 61, 1.
Klein, H. and D. Woermann (1976), J. Chem. Phys. 64, 5316.
Lee, S. P. (1978), Chem. Phys. Lett. 57, 611.
Lee, T. and C. N. Yang (1952), Phys. Rev. 87, 410.
Le Guillou, J. C. and J. Zinn-Justin (1977), Phys. Rev. Lett. 39, 95.
Le Guillou, J. C. and J. Zinn-Justin (1980), Phys. Rev. B 21, 3976.
Leung, S. S. and R. B. Griffiths (1973), Phys. Rev. A 8, 2670.
Levelt Sengers, J. M. H. (1974), Physica 73, 73.
Levelt Sengers, J. M. H. (1975), in Experimental Thermodynamics Vol. II, B. Le Neindre and B. Vodar, eds. (Butterworth, London) p. 657.
Levelt Sengers, J. M. H. , W. L. Greer and J. V. Sengers (1976), J. Phys. Chem. Ref. Data 5, 1.
Levelt Sengers, J. M. H. and J. V. Sengers (1975), Phys. Rev. A 12, 2622.
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).
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).
Ley-Koo, M. and M. S. Green (1977), Phys. Rev. A 16, 2483.
Lin, J. S. and P. W. Schmidt (1974), Phys. Rev. A 10, 2290.
Lipa, J. A., C. Edwards and M. S. Buckingham (1977), Phys. Rev. A 15, 778.
Lunacek, J. H. and D. S. Cannell (1971), Phys. Rev. Lett. 27, 841.
Mazenko, G. (1978), in Correlation Functions and Quasiparticle Interactions, J. W. Halley, ed. (Plenum Publ. Corp., New York) p. 1.
McKenzie, S. (1979), J. Phys. A 12, L185.
Mermin, N. D. (1971), Phys. Rev. Lett. 26, 957.
Mermin, N. D. and J. J. Rehr (1971), Phys. Rev. Lett. 26, 1155.
Mistura, L. (1979), Nuovo Cim. 52B, 277.
Moldover, M. R. (1969), Phys. Rev. 182, 342.
Moldover, M. R. , J. V. Sengers, R. W. Gammon and R. J. Hocken (1979), Rev. Mod. Phys. 51, 79.
Moore, M. A. , D. Jasnow and M. Wortis (1969), Phys. Rev. Lett. 22, 940.
Morrison, G. and C. M. Knobler (1976), J. Chem. Phys. 65, 5507.
Nagarajan, N., A. Kumar, E. S. R. Gopal and S. C. Greer (1980), J. Phys. Chem. 84, 2883.
Nakata, M. , T. Dobashi, N. Kuwara, M. Kaneko and B. Chu (1978), Phys. Rev. A 18, 2683.
Nickel, B. G. and B. Sharpe (1979), J. Phys. A 12, 1819.
Nicoll, J. F. (1980), Phys. Rev. A (in press).
Nicoll, J. F. and R. K. P. Zia (1980), Phys. Rev. B (in press).
Ohta, T. (1977), J. Phys. C 10, 791.
Oitmaa, J. and J. Ho-Ting-Hun (1979), J. Phys. A 12, L281.
Oxtoby, D. W. and W. M. Gelbart (1974), J. Chem. Phys. 61, 2957.
Patashinkii, A. Z. and V. I. Pokrovskii (1979), Fluctuation Theory of Phase Transitions (Pergamon Press, New York).
Pelger, M., H. Klein and D. Woermann (1977), J. Chem. Phys. 67, 5362.
Pfeuty, P. and G. Toulouse (1977), Introduction to the Renormalization Group and to Critical Phenomena (Wiley, New York).
Pittman, C., T. Doiron and H. Meyer (1979), Phys. Rev. B 20, 3678.
Rehr, J. J. (1979), J. Phys. A 12, L179.
Rehr, J. J. and N. D. Mermin (1973), Phys. Rev. A 8, 472.
Rowlinson, J. S. (1969), Nature 224, 541.
Saam, W. F. (1970), Phys. Rev. A 2, 1461.
Scheibner, B. A., C. M. Sorensen, D. T. Jacobs, R. C. Mockler and W. J. O’Sullivan (1978), Chem. Phys. 31, 209.
Schmidt, H. H. (1971), J. Chem. Phys. 54, 3610.
Schneider, R., L. Belkoura, J. Schelten, D. Woermann and B. Chu (1980), Phys. Rev. A (in press).
Scott, R. L. (1978), in Chemical Thermodynamics, Vol. 2, Specialist Periodical Report, M. L. McGlashnan, ed. (Chemical Society, London), p. 238.
Sengers, J. V. (1972), Ber. Bunsenges. physik. Chemie 76, 234.
Sengers, J. V., D. Bedeaux, P. Mazur and S. C. Greer (1980), Physica A (in press).
Sengers, J. V. and P. H. Keyes (1971), Phys. Rev. Lett. 26, 70.
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.
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.
Sengers, J. V. and M. R. Moldover (1978b), Phys. Lett. 66A, 44.
Sheludyak, Yu. E. and V. A. Rabinovich (1979), High Temp. 17, 40.
Siggia, E. D., B. I. Halperin, and P. C. Hohenberg (1976), Phys. Rev. B 13, 2110.
Sorensen, C. M. , R. C. Mockley and W. J. O’Sullivan (1978), Phys. Rev. Lett. 40, 777.
Stauffer, D., M. Ferer and M. Wortis (1972), Phys. Rev. Lett. 29, 345.
Stein, A. and G. F. Allen (1974), J. Phys. Chem. Ref. Data 2, 443.
Swinney, H. L. and D. L. Henry (1973), Phys. Rev. A 8, 2586.
Thijsse, B. J. (1980), to be published.
Thoen, J. , E. Bloemen and W. Van Dael (1978), J. Chem. Phys. 68, 735.
Tsai, B. C. and D. McIntyre (1974), J. Chem. Phys. 60, 937.
Vause, C. and J. Sak (1980), Phys. Lett. 77A, 191; Phys. Rev. A 21, 2099.
Wallace, D. J. and R. K. P. Zia (1974), J. Phys. C 7, 3480.
Warkulwiz, V. P., B. Mozer and M. S. Green (1974), Phys. Rev. Lett. 32, 1410.
Wegner, F. J. (1972a), Phys. Rev. B 5, 4529.
Wegner, F. J. (1972b), Phys. Rev. B 6 1891.
Wegner, F. J. (1975), J. Phys. A 8, 710.
Wheeler, J. C. (1977), Ann. Rev. Phys. Chem. 28, 411.
Widom, B. (1965), J. Chem. Phys. 43, 3898.
Widom, B. and J. S. Rowlinson (1970), J. Chem. Phys. 52, 1670.
Wilcox, L. R. and D. Balzarini (1968), J. Chem. Phys. 48, 753.
Wilson, K. G. and J. Kogut (1974), Physics Reports 12C, 75.
Zinn-Justin, J. (1979), J. Physique 40, 63.
Zollweg, J. A. and G. W. Mulholland (1972), J. Chem. Phys. 57, 1021.
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Sengers, J.V. (1982). Universality of Critical Phenomena in Classical Fluids. In: Lévy, M., Le Guillou, JC., Zinn-Justin, J. (eds) Phase Transitions Cargèse 1980. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3347-0_4
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