History of the Lenz-Ising model 1965-1971: The role of a simple model in understanding critical phenomena

Archive for History of Exact Sciences

Volumn 65, Issue 6, 2011, Pages 625-658

  Niss, Martin ^a  

^a ROSKILDE UNIVERSITY   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 80355144506     PISSN: 00039519     EISSN: 14320657     Source Type: Journal    
DOI: 10.1007/s00407-011-0086-1     Document Type: Article

References (81)

1. Als-Nielsen J., Dietrich O. W. (1967a) Pair-correlation function in disordered β-brass as studied by neutron diffraction. Physical Review153: 706-710.
2. Als-Nielsen, J., and O. W. Dietrich. 1967b. Long-range order and critical scattering of neutrons below the transition temperature in β-brass. Physical Review153: 717-721.
3. Anisimov, M. 1998. Talk at the symposium on the History of Critical Phenomena, March APS Meeting, 20 March 1998. Report published in History of Physics Newsletter VII(3).
4. Ashrafi, B., K. Hall, and S. S. Schweber. n. d. The solution to the phase transition problem: 1965-1975 (unpublished).
5. Batterman R. W. (2002) Asymptotics and the role of minimal models. British Journal of Philosophy of Science 53: 21-38.
6. Binney J. J., Dowrick N. J., Fisher A. J., Newman M. E. J. (1999) The theory of critical phenomena, An introduction to the renormalization group. Clarendon Press, Oxford.
7. Burley D. M. (1960) Some magnetic properties of the Ising model. Philosophical Magazine 5: 909-919.
8. Cahn J. W., Hilliard J. E. (1958) Free energy of a nonuniform system. I. Interfacial energy. Journal of Chemical Physics 28: 258-267.
9. Dietrich O. W., Als-Nielsen J. (1967) Temperature dependence of short-range order in β-brass. Physical Review153: 711-717.
10. Domb C. (1955) Statistical physics and its problems. Science Progress 43: 402-417.
11. Domb C. (1991) Michael E. Fisher at King's college London. Physica A 177: 1-21.
12. Domb C. (1996) The critical point. Taylor and Francis, London.
13. Domb C. (2003) Some observations on the early history of equilibrium statistical mechanics. Journal of Statistical Physics 110: 475-496.
14. Domb C., Hunter D. L. (1965) On the critical behaviour of ferromagnets. Proceedings of the Physical Society 86: 1147-1151.
15. Domb C., Sykes M. F. (1957) On the susceptibility of a ferromagnetic above the Curie point. Proceedings of the Royal Society of London A 240: 214-228.
16. Domb C., Sykes M. F. (1962) Effect of change of spin on critical properties of Ising and Heisenberg models. Physical Review128: 168-173.
17. Essam J. W., Fisher M. E. (1963) Padé approximant studies of the lattice gas and Ising ferromagnet below the critical point. Journal of Chemical Physics 38: 802-812.
18. Fisher M. E. (1959) The susceptibility of the plane Ising model. Physica 25: 521-524.
19. Fisher M. E. (1962) On the theory of critical point density fluctuations. Physica 28: 172-180.
20. Fisher M. E. (1964) Correlation functions and the critical region of simple fluids. Journal of Mathematical Physics 5: 944-962.
21. Fisher, M. E. 1965. The nature of critical points. In Lectures in theoretical physics, Vol. VIIC, ed. W. E. Brittin. Boulder: University of Colorado Press.
22. Fisher, M. E. 1966a. Notes, definitions, and formulas for critical point singularities. In Critical phenomena. Proceedings of a conference held in Washington, DC, April 1965, ed. M. S. Green and J. V. Sengers, 21-25. Washington, DC: National Bureau of Standards.
23. Fisher, M. E. 1966b. Theory of critical fluctuations and singularities. In Critical phenomena. Proceedings of a conference held in Washington, DC, April 1965, ed. M. S. Green and J. V. Sengers, 108-116. Washington, DC: National Bureau of Standards.
24. Fisher M. E. (1967a) The theory of equilibrium critical phenomena. Reports on Progress in Physics 30: 615-730.
25. Fisher M. E. (1967b) The theory of condensation and the critical point. Physics 3: 255-283.
26. Fisher, M. E. 1983. Scaling, universality and renormalization group theory. In Critical Phenomena, Lecture Notes in Physics, Vol. 186, ed. F. J. W. Hahne, 1-139. Berlin: Springer.
27. Fisher M. E. (1998) Renormalization group theory: Its basis and formulation in statistical physics. Reviews of Modern Physics 70: 653-681.
28. Fisher M. E., Burford R. (1967) Theory of critical-point scattering and correlations. I. The Ising model. Physical Review156: 583-622.
29. Goldenfeld N. (1992) Lectures on phase transitions and the renormalization group. Perseus Books, Reading.
30. Green M. S. (1960) On the theory of the critical point of a simple fluid. Journal of Chemical Physics 33: 1403-1409.
31. Green, M. S. 1966. Introduction. In Critical phenomena. Proceedings of a conference held in Washington, DC, April 1965, ed. M. S. Green and J. V. Sengers, ix-xi. Washington, DC: National Bureau of Standards.
32. Griffiths R. B. (1964) Peierls proof of spontaneous magnetization in a two-dimensional Ising ferromagnet. Physical Review136: A437-A439.
33. Griffiths R. B. (1966) Spontaneous magnetization in idealized ferromagnets. Physical Review152: 240-246.
34. Griffiths R. B. (1967a) Correlations in Ising ferromagnets. I. Journal of Mathematical Physics 8: 478-483.
35. Griffiths R. B. (1967b) Correlations in Ising ferromagnets. II. External magnetic fields. Journal of Mathematical Physics 8: 484-490.
36. Griffiths R. B. (1970) Dependence of critical indices on a parameter. Physical ReviewLetters 24: 1479-1482.
37. Guggenheim E. A. (1945) The principle of corresponding states. Journal of Chemical Physics 13: 253-261.
38. Guggenheim E. A. (1950) Thermodynamics. North Holland Publication, Amsterdam.
39. Jasnow D., Wortis M. (1968) High-temperature critical indices for the classical anisotropic Heisenberg model. Physical Review176: 739-750.
40. Kadanoff L. P. (1966a) Scaling laws for Ising models near Tc. Physics 2: 263-272.
41. Kadanoff L. P. (1966b) Spin-spin correlation in the two-dimensional Ising model. Nuovo Cimento 44: 276-304.
42. Kadanoff, L. P. 1971. Critical behavior. Universality and scaling. In Critical Phenomena, ed. M. S. Green. Proceedings of the International School 'Enrico Fermi' 51, Italian Physical Society, 100-117. New York: Academic Press.
43. Kadanoff, L. P. 1976. Scaling, universality, and operator algebras. In Phase transitions and critical phenomena, Vol. 5A, ed. C. Domb, and M. S. Green, 1-34. New York: Academic Press.
44. Kadanoff L. P. (1999) From order to chaos II: Essays: Critical, chaotic and otherwise. World Scientific, Singapore.
45. Kadanoff L. P. (2009) More is the same; mean field theory and phase transitions. Journal of Statistical Physics 137: 777-797.
46. Kadanoff L. P., Götze W., Hamblen D., Hecht R., Lewis R. E. A. S., Palciauskas V. V., Rayl M., Swift J., Aspnes D., Kane J. W. (1967) Static phenomena near critical points: Theory and experiment. Reviews of Modern Physics 39: 395-432.
47. Kaufman B., Onsager L. (1949) Crystal statistics. III. Short-range order in a binary Ising lattice. Physical Review76: 1244-1252.
48. Laramore G. E. (1970) A report on the midwinter solid-state research conference. Journal of Statistical Physics 2: 107-110.
49. Lee T. D., Yang C. N. (1952) Statistical theory of equations of state and phase transitions. II. Lattice gas and Ising model. Physical Review87: 410-419.
50. Levelt Sengers J. M. H. (1979) Liquidons and gasons: Controversies about the continuity of states. Physica 98: 363-402.
51. Levelt Sengers J. M. H., Hocken R., Sengers J. V. (1977) Critical-point universality and fluids. Physics Today 30: 42-96.
52. Münster, A. 1965. Critical fluctuations. In Fluctuation phenomena in solids, ed. R. E. Burgess, 180-266. New York: Academic Press.
53. Nagle J. F., Bonner J. C. (1970) Numerical studies of the Ising chain with long-range ferromagnetic interactions. Journal of Physics C 3: 352-366.
54. Niss M. (2005) History of the Lenz-Ising model 1920-1950: From ferromagnetic to cooperative phenomena. Archive for History of Exact Science 59: 267-318.
55. Niss M. (2009) History of the Lenz-Ising model 1950-1965: from irrelevance to relevance. Archive for History of Exact Science 63: 243-287.
56. Onsager L. (1944) Crystals statistics. I. A two-dimensional model with an order-disorder transition. Physical Review65: 117-149.
57. Pais A. (1982) Subtle is the Lord: The science and life of Albert Einstein. Oxford University Press, Oxford.
58. Patashinskii A. Z., Pokrovskii V. L. (1966) Behavior of ordered systems near transition point. Soviet Physics JETP 23, 292. English trans. of Zhurnal Eksperimental'noi i Teoreticheskoi Fiziki 50: 439.
59. Peierls R. (1980) Model-making in physics. Contemporary Physics 21: 3-17.
60. Pokrovsky V. L. (1998) Notes on history of critical phenomena. History of Physics Newsletter VII(3): 15-18.
61. Rice O. K. (1955) Shape of the coexistence curve near the critical temperature. Journal of Chemical Physics 23: 164-168.
62. Rushbrooke G. S. (1963) On the thermodynamics of the critical region for the Ising problem. Journal of Chemical Physics 39: 842-843.
63. Rushbrooke G. S., Wood P. J. (1958) On the Curie points and high-temperature susceptibilities of Heisenberg model ferromagnetics. Molecular Physics 1: 257-283.
64. Sengers J. V., Shanks J. G. (2009) Experimental critical-exponent values for fluids. Journal of Statistical Physics 137: 857-877.
65. Schweber S. S., Wächter M. (2000) Complex systems, modelling and simulation. Studies in the History and Philosophy of Modern Physics 31: 583-609.
66. Stanley H. E. (1971) Introduction to phase transitions and critical phenomena. Oxford University Press, New York, Oxford.
67. Stanley H. E. (1999) Scaling, universality, and renormalization: Three pillars of modern critical phenomena. Reviews of Modern Physics 71: S358-S366.
68. Stanley H. E., Hankey A., Lee M. H. (1971). Scaling, transformation and universality. In Critical Phenomena, ed. M. S. Green. Proceedings of the International School of Physics 'Enrico Fermi' 51 Italian Physical Society, 237-264. New York, London: Academic Press.
69. Stillinger F. H., Frisch H. L. (1961) Critique of cluster theory of critical point density fluctuations. Physica 27: 751-752.
70. Temperley H. N. V. (1956) Changes of state. Cleaver-Hume, London.
71. Trac C. A., McCoy B. M. (1975) Examination of the phenomenological scaling functions for critical scattering. Physical ReviewB 12: 368-387.
72. Widom B. (1962) Relation between the compressibility and the coexistence curve near the critical point. Journal of Chemical Physics 37: 2703-2704.
73. Widom B. (1964) Degree of the critical isotherm. Journal of Chemical Physics 41: 1633-1634.
74. Widom B. (1965a) Surface tension and molecular correlations near the critical point. Journal of Chemical Physics 43: 3892-3897.
75. Widom B. (1965b) Equation of state in the neighborhood of the critical point. Journal of Chemical Physics 43: 3898-3905.
76. Widom B. (1974) The critical point and scaling theory. Physica 73: 107-118.
77. Widom B. (2011) Laboring in the vineyard of physical chemistry. Annual Reviews of Physical Chemistry 62: 1-18.
78. Widom, B., B. Ashrafi, and S. Schweber. 2003. Interview, March 2003, history of recent science and technology, the Dibner institute for the history of science and technology, MIT, Massachusetts. http://authors. library. caltech. edu/5456/1/hrst. mit. edu/hrs/renormalization/Widom/. Accessed 10 May 2010.
79. Yang C. N., Lee T. D. (1952) Statistical theory of equations of state and phase transitions. I. Theory of condensation. Physical Review87: 404-409.
80. Yang C. N., Yang C. P. (1964) Critical point in liquid-gas transitions. Physical ReviewLetters 13: 303-305.
81. Ziman J. M. (1965) Mathematical models and physical toys. Nature 206: 1187-1192.