Recent developments in phase transitions and critical phenomena

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.

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References

  1. 1

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

    ADS  CAS  Article  Google Scholar 

  2. 2

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

    ADS  CAS  Article  Google Scholar 

  3. 3

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

    Google Scholar 

  4. 4

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

    ADS  CAS  Article  Google Scholar 

  5. 5

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

  6. 6

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

    ADS  Google Scholar 

  7. 7

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

    Article  Google Scholar 

  8. 8

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

    ADS  Article  Google Scholar 

  9. 9

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

    ADS  MathSciNet  CAS  Article  Google Scholar 

  10. 10

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

    ADS  Article  Google Scholar 

  11. 11

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

    ADS  CAS  Article  Google Scholar 

  12. 12

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

    ADS  Article  Google Scholar 

  13. 13

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

    ADS  Article  Google Scholar 

  14. 14

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

    ADS  Article  Google Scholar 

  15. 15

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

    ADS  Article  Google Scholar 

  16. 16

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

    ADS  CAS  Article  Google Scholar 

  17. 17

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

    ADS  Article  Google Scholar 

  18. 18

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

    ADS  Article  Google Scholar 

  19. 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. 20

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

    ADS  Article  Google Scholar 

  21. 21

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

    ADS  Article  Google Scholar 

  22. 22

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

    ADS  Article  Google Scholar 

  23. 23

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

    ADS  Article  Google Scholar 

  24. 24

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

    ADS  Article  Google Scholar 

  25. 25

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

    ADS  Article  Google Scholar 

  26. 26

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

    ADS  Article  Google Scholar 

  27. 27

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

    ADS  CAS  Article  Google Scholar 

  28. 28

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

    ADS  Article  Google Scholar 

  29. 29

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

    Article  Google Scholar 

  30. 30

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

    Google Scholar 

  31. 31

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

    ADS  Article  Google Scholar 

  32. 32

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

    Article  Google Scholar 

  33. 33

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

    ADS  Article  Google Scholar 

  34. 34

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

    ADS  MathSciNet  Google Scholar 

  35. 35

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

    ADS  Article  Google Scholar 

  36. 36

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

    Google Scholar 

  37. 37

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

    Google Scholar 

  38. 38

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

    ADS  CAS  Google Scholar 

  39. 39

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

    ADS  Google Scholar 

  40. 40

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

  41. 41

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

    ADS  Article  Google Scholar 

  42. 42

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

    ADS  CAS  Article  Google Scholar 

  43. 43

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

    ADS  CAS  Google Scholar 

  44. 44

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

    ADS  CAS  Article  Google Scholar 

  45. 45

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

    Google Scholar 

  46. 46

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

    ADS  CAS  Article  Google Scholar 

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

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