Skip to main content
SpringerLink
Log in

Recent developments in phase transitions and critical phenomena

  • Review Article
  • Published:

From Nature

View current issue Submit your manuscript

Abstract

Universal dimensionless numbers characterise singularities at the critical point in magnets, binary mixtures and alloys, superfluids, and in a variety of other systems. A desire to understand these numbers has stimulated a significant breakthrough in the analysis of statistical mechanical partition sums. Critical phenomena can now be understood in terms of universality, Hamiltonian flows, and renormalisation group recursion relations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Fisher, M. E. Rept. Progr. Phys. 30, 615–730 (1967).

    Article  ADS  CAS  Google Scholar 

  2. Kadanoff, L. P. et al. Rev. mod. Phys. 39, 395–431 (1967).

    Article  ADS  CAS  Google Scholar 

  3. Stanley, H. E. Introduction to Phase Transitions and Critical Phenomena (Oxford, New York and Oxford, 1971).

    Google Scholar 

  4. Heller, P. Rept. Progr. Phys. 30, 731–826 (1967).

    Article  ADS  CAS  Google Scholar 

  5. Domh, C. & Green, M. S. (eds) Phase Transitions and Critical Phenomena 3, (Academic, New York, 1975).

  6. Wilson, K. G. Pnys. Rev. B4, 3174–3183 and 3184–3205 (1971).

    ADS  Google Scholar 

  7. Kadanoff, L. P. Physics 2, 263–272 (1966).

    Article  Google Scholar 

  8. Stanley, H. E. Phys. Rev. 179, 570–577 (1969).

    Article  ADS  Google Scholar 

  9. Onsager, L. Phys. Rev. 65, 117–149 (1944).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  10. Niemeyer, Th. & van Leeuwen, J. M. J. Phys. Rev. Lett. 31, 1411–1414 (1973): Physica, 71, 17–40 (1974).

    Article  ADS  Google Scholar 

  11. Rudnick, J. Phys. Rev. B11, 363–376 (1975).

    Article  ADS  CAS  Google Scholar 

  12. Nauenberg, M. & Nienhuis, B. Phys. Rev. Lett. 33, 1598–1601 (1974).

    Article  ADS  Google Scholar 

  13. Nelson, D. R. Phys. Rev. B11, 3504–3519 (1975).

    Article  ADS  Google Scholar 

  14. Wilson, K. G. & Kogut, J. Phys. Rep. 12C, 77–199 (1974).

    Article  ADS  Google Scholar 

  15. Wilson, K. G. Rev. mod. Phys. 47, 773–840 (1975).

    Article  ADS  Google Scholar 

  16. Kadanoff, L. P. & Houghton, A. Phys. Rev. B11, 377–386 (1975).

    Article  ADS  CAS  Google Scholar 

  17. Kadanoff, L. P. Phys. Rev. Lett. 34,, 1005–1008 (1975).

    Article  ADS  Google Scholar 

  18. Kadanoff, L. P., Houghton, A. & Yalabik, M. C. J. stat. Phvs. 14, 171–203 (1976).

    Article  ADS  Google Scholar 

  19. Landau, L. D. Phys. Zurn. Sowjetunion 11, 26–35, 545–567 (1937) [English translation: ter Haar. D. (ed.) Men of Physics: L. D. Landau, vol. II (Pergamon, Oxford, 1969).

    Google Scholar 

  20. Wegner, F. J. Phys. Rev. B5, 4529–4536 (1972).

    Article  ADS  Google Scholar 

  21. Wilson, K. G. & Fisher, M. E. Phys. Rev. Lett. 28, 240–243 (1972).

    Article  ADS  Google Scholar 

  22. Wilson, K. G. Phys. Rev. Lett. 28, 548–551 (1972).

    Article  ADS  Google Scholar 

  23. Ma, S.-K. Phys. Rev. Lett. 29, 1311–1314 (1972).

    Article  ADS  Google Scholar 

  24. Abe, R. Prog. theor. Phys. 48, 1414–1415 (1972); ibid. 49, 113–128 (1973).

    Article  ADS  Google Scholar 

  25. Abe, R. & Hikami, S. Prog. theor. Phys. 49, 442–452 (1973).

    Article  ADS  Google Scholar 

  26. Ma, S.-K. Rev. mod. Phys. 45, 589–614 (1973).

    Article  ADS  Google Scholar 

  27. Fisher, M. E. Rev. mod. Phys. 46, 597–616 (1974).

    Article  ADS  CAS  Google Scholar 

  28. Barber, M. Phys. Rep. 29C, 3–84 (1977).

    Article  ADS  Google Scholar 

  29. Polyakov, A. M. Phys. Lett. 59B, 79–81 (1975).

    Article  Google Scholar 

  30. Migdal, A. A. Zh. E. T. F. 69, 1457–1463 (1975).

    Google Scholar 

  31. Brézin, E. & Zinn-Justin, J. Phys. Rev. Lett. 36, 691–694 (1976): Phys. Rev. B14, 3110–3120 (1976).

    Article  ADS  Google Scholar 

  32. Pelcovits, R. A. & Nelson, D. R. Phys. Lett. 57A, 23–25 (1976): Phys. Rev. B (in the press).

    Article  Google Scholar 

  33. Brézin, E., Zinn-Justin, J. & Le Guillon, J. C. Phys. Rev. B14, 4976–4978 (1976).

    Article  ADS  Google Scholar 

  34. Kadanoff, L. P. A. Phys. 100, 359–394 (1976).

    ADS  MathSciNet  Google Scholar 

  35. Wegner, F. J. Z. Phys. 206, 465–470 (1967).

    Article  ADS  Google Scholar 

  36. Berezinskii, V. L. Zh. Eksp. Tero. Fiz. 59, 907–920 (1970). [Sov Phys. JETP 32, 493–500 (1971)].

    Google Scholar 

  37. Berezinskii, V. L. Zh. Eksp. Tero. Fiz. 61, 1144–1156 (1971). [Sov. Phys. JETP 34, 610–616 (1971)].

    Google Scholar 

  38. Kosterlitz, J. M., Thouless, D. J. J. Phys. C6, 1181–1203 (1973).

    ADS  CAS  Google Scholar 

  39. Kosterlitz, J. M. J. Phys. C7, 1046–1060 (1974).

    ADS  Google Scholar 

  40. José, J., Kadanoff, L. P., Kirkpatrick, S. & Nelson, D. R. Phys. Rev. B (in the press).

  41. Gell-Mann, M. & Low, F. E. Phys. Rev. 95, 1300–1312 (1954).

    Article  ADS  Google Scholar 

  42. Wilson, K. G. Phys. Rev. D10, 2445–2459 (1974).

    Article  ADS  CAS  Google Scholar 

  43. Anderson, P. W. J. Phys. C3, 2436–2441 (1970).

    ADS  CAS  Google Scholar 

  44. Licciardello, D. C. & Thouless, D. J. Phys. Rev. Lett. 35, 1475–1478 (1975).

    Article  ADS  CAS  Google Scholar 

  45. Wegner, F. J. Z. Phys. B25, 327–337 (1976).

    Google Scholar 

  46. Hohenberg, P. C. & Halperin, B. I. Rev. mod. Phys. 49, 435–479 (1977).

    Article  ADS  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Lyman Laboratory of Physics, Harvard University, Cambridge, Massachusetts, 02138

    David R. Nelson

Authors
  1. David R. Nelson
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nelson, D. Recent developments in phase transitions and critical phenomena. Nature 269, 379–383 (1977). https://doi.org/10.1038/269379a0

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1038/269379a0

  • Springer Nature Limited

Search

Navigation