Critical Phenomena for Field Theorists

  • Steven Weinberg
Part of the The Subnuclear Series book series (SUS, volume 14)


Many of us who are not habitually concerned with problems in statistical physics have gradually been becoming aware of dramatic progress in that field. The mystery surrounding the phenomenon of second-order phase transitions seems to have lifted, and theorists now seem to be able to explain all sorts of scaling laws associated with these transitions, and even (more or less) to calculate the “critical exponents” of the scaling laws.1 Furthermore, the methods used to solve these problems appear to have a profound connection with the methods of field theory — one overhears talk of “renormalization group equations”, “infrared divergences”, “ultraviolet cut-offs”, and so on. It is natural to conclude that field theorists have a lot to learn from their statistical brethren.


Partition Function Boson Mass Critical Phenomenon Finite Temperature Coupling Function 
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  1. 1.
    For surveys of the modern theory of critical phenomena, including references to the original literature, see the following reviews: K. G. Wilson and J. K.gut, Physics Reports 12C, No. 2 (1974).Google Scholar
  2. M. E. Fisher, Rev. Mod. Phys. 46, 597 (1974).ADSCrossRefGoogle Scholar
  3. E. Brézin, J. C. Le Guillou, and J. Zinn-Justin, in Phase Transitions and Critical Phenomena, ed. by C. Domb and M. S. Green (Academic Press, New York, 1975 ), Vol. VI.Google Scholar
  4. F. J. Wegner, in Trends in Elementary Particle Theory ( Springer-Verlag, Berlin, 1975 ), p. 171.Google Scholar
  5. K. Wilson, Rev. Mod. Phys. 47, 773 (1975).ADSCrossRefGoogle Scholar
  6. Shang-Keng Ma, Modern Theory of Critical Phenomena (W. A. Benjamin, Inc., Reading, Mass., 1976 ).Google Scholar
  7. 2.
    A. L. Fetter and J. D. Walecka, Quantum Theory of Many-Particle Systems (McGraw-Hill, Inc., New York, 1971 ), Chapter 7.Google Scholar
  8. 3.
    S. Weinberg, Phys. Rev. D9, 3357 (1974.)Google Scholar
  9. L. Dolan and R. Jackiw, Phys. Rev. D9, 3320 (1974).ADSGoogle Scholar
  10. D. A. Kirzhnits and A. D. Linde, Zh. Eksp. Teor. Fiz. 67, 1263 (1974).ADSGoogle Scholar
  11. C. W. Bernard, Phys. Rev. D9, 3312 (1974).ADSGoogle Scholar
  12. 4.
    F. Bloch and A. Nordsieck, Phys. Rev. 52, 54 (1937).ADSCrossRefGoogle Scholar
  13. For a version in modern notation, see S. Weinberg, Phys. Rev. 140, B516 (1965).MathSciNetADSCrossRefGoogle Scholar
  14. 5.
    M. Gell-Mann and F. E. Low, Phys. Rev. 95, 1300 (1954).MathSciNetADSzbMATHCrossRefGoogle Scholar
  15. 6.
    The fixed point in the nonlinear σ-model in 2 + ε dimensions has been under intensive study lately; see W. A. Bardeen, B. W. Lee, and R. E. Shrock, Fermilab-Pub-76/33-THY, March 1976.Google Scholar
  16. E. Brézin, J. Zinn-Justin, and J. C. Le Guillou, Saclay preprints, May 1976. The motivation of these studies appears to be quite different from that described here.Google Scholar
  17. 7.
    F. J. Wegner and A. Houghton, Phys. Rev. A 8, 401 (1973).ADSCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1978

Authors and Affiliations

  • Steven Weinberg
    • 1
  1. 1.Lyman Laboratory of PhysicsHarvard UniversityCambridgeUSA

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