More is the same; phase transitions and mean field theories

Journal of Statistical Physics

Volumn 137, Issue 5, 2009, Pages 777-797

  Kadanoff, Leo P ^a  

^a UNIVERSITY OF CHICAGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 74549195569     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-009-9814-1     Document Type: Article

References (66)

1. Anderson, P. W.: More is different. Sci. New Ser. 177(4047), 393-396 (1972).
2. Ong, N.-P., Bhatt, R. (eds.): More is Different: Fifty Years of Condensed Matter Physics. Princeton Series in Physics. Princeton University Press, Princeton (2001).
3. van Till, H. J.: Basil, Augustine, and the Doctrine of Creation's Functional Integrity. Sci. Christ. Belief 8(1), 21-38 (1996).
4. Ehrenfest, P.: Proc. K. Akad. Akad. Wet. Amst. 36, 147 (1933).
5. Daugherty, D.: Elaborating the crystal concept: scientific modeling and ordered states of matter. PhD Thesis, Committee on Conceptual and Historical Studies of Science, University of Chicago (2007).
6. Willard Gibbs, J.: Elementary Principles of Statistical Mechanics. Scribner's, New York (1902).
7. Bumstead, H. A., van Name, R. G. (eds.): Scientific Papers of J. Willard Gibbs, 2 vols. (1961). ISBN 0918024773.
8. Domb, C.: The Critical Point. Taylor & Francis, London (1996).
9. Ising, E.: Z. Phys. 31, 253 (1925).
10. Brush, S. G.: History of the Lenz-Ising Model. Rev. Mod. Phys. 39, 883-893 (1967).
11. Gallavotti, G.: Entropy, nonequilibrium, chaos and infinitesmals, p. 54 in [12].
12. Gallavotti, G., Reiter, W. L., Ygnvason, J. (eds.): Boltzmann's Legacy. European Mathematical Society (2008).
13. Wightman, A.: On the prescience of J. Willard Gibbs. In Caldi, D. G., Mostow, G. D. (eds.) Proceedings of the Gibbs Symposium, Yale University May 15-17, 1989. American Mathematical Society and American Institute of Physics (1989).
14. Uhlenbeck, G. E.: Some historical and critical remarks about the theory of phase transitions. In: Fujita, S. (ed.) Science of Matter: Festschrift in Honor of Professor Ta-You Wu. Gordon & Breach, New York (1978).
15. Cohen, E. G. D.: Private communication.
16. Ruelle, D.: Statistical Mechanics: Rigorous Results. World Scientific, Singapore (1969).
17. Dunkel, J., Hilbert, S.: Phase transition in small systems: microcanonical vs. canonical ensembles. arXiv: cond-mat/0511501v4.
18. www.phys.au.dk/~fogedby/statphysII/no-PT-in-1D.pdf.
19. Peierls, R.: Proc. Camb. Philos. Soc. 32, 477 (1936).
20. Griffiths, R.: Peierls proof of spontaneous magnetization in a two-dimensional Ising ferromagnet. Phys. Rev. 136, A437-A439 (1964).
21. Batterman, R. W.: Idealization and Modeling. Synthesis doi: 10. 1007. http://www. romanfrigg. org/Links/MS1/Synthese_MS1_Batterman. pdf.
22. Batterman, R. W.: The Devil in the Details. Oxford University Press, New York (2002).
23. Berry, M. V.: Asymptotics, singularities and the reduction of theories. In: Prawitz, D., Skyrms, B., Westerstahl, D. (eds.) Proc. 9th Int. Cong. Logic, Method., and Phil. of Sci., vol. IX, pp. 597-607 (1994).
24. Curie, P.: Ann. Chem. Phys. 5, 289 (1895).
25. Weiss, P.: J. Phys. 6, 661 (1907).
26. Maxwell, J. C.: Nature 10, 407 (1874) 11 418 (1875).
27. Onsager, L.: Phys. Rev. 65, 117 (1944).
28. Yang, C. N.: Phys. Rev. 85, 808 (1952).
29. van der Waals, J. D.: Thesis Leiden (1873).
30. http://en. wikipedia. orgwikiVan_der_Waals_equation.
31. Sengers, J. L.: How Fluids Unmix. Koninklijke Nederlandse Akademie van Wetenschappen, Amsterdam (2002).
32. Andrews, T.: On the continuity of the gaseous and liquid states of matter. Philos. Trans. R. Soc. 159, 575-590 (1869). Reprinted in: T. Andrews, The Scientific Papers. Macmillan, London (1889).
33. Nagel, E.: The Structure of Science. Routledge & Kegan Paul, London (1961).
34. Batterman, R. W.: Reduction. In: Bouchart, D. (ed.) Encyclopedia of Philosophy, 2nd edn. Macmillan, Detroit (2006).
35. Schrödinger, E.: Statistical Thermodynamics. Cambridge University Press, Cambridge (1957).
36. Kuhn, T. S.: The Structure of Scientific Revolutions, 1st. edn. University of Chicago Press, Chicago (1962).
37. Bragg, W. L., Williams, E. J.: The effect of thermal agitation on atomic arrangement in alloys. Proc. R. Soc. Lond. A 145, 699-730 (1934).
38. Bardeen, J., Cooper, L. N., Schrieffer, J. R.: Microscopic theory of superconductivity. Phys. Rev. 106, 162-164 (1957).
39. Bardeen, J., Cooper, L. N., Schrieffer, J. R.: Theory of superconductivity. Phys. Rev. 108, 1175 (1957).
40. Néel, L.: Propriétées magnétiques des ferrites; Férrimagnétisme et antiferromagnétisme. Ann. Phys. Paris 3, 137-198 (1948).
41. Griffin, A.: arXiv: cond-mat/9901123v1, 13 Jan 1999.
42. Landau, L. D.: Phys. Z. Sow. 11, 26545 (1937). English Translation: Collected Papers of Landau, L. D., ter Haar, D. (eds.), pp. 193-215. Pergamon Press, Oxford (1965).
43. Kadanoff, L. P., Gotze, W., Hamblen, D., Hecht, R., Lewis, E. A. S., Palciauskas, V. V., Rayl, M., Swift, J., Aspnes, D., Kane, J. W.: Static Phenomena Near Critical Points: Theory and Experiment. Rev. Mod. Phys. 39, 395 (1967).
44. Milton, K. A., Schwinger, J.: Electromagnetic Radiation: Variational Methods, Waveguides and Accelerators: Including Seminal Papers of Julian Schwinger. Springer, Berlin (2006). ISBN: 3540292233.
45. Galison, P.: Image and Logic: A Material Culture of Microphysics, p. 820. University of Chicago Press, Chicago (1997). ISBN 0226279170, 9780226279176.
46. Feynman, R. P., Hibbs, A. R.: Quantum Mechanics and Path Integrals. McGraw-Hill, New York (1965). ISBN 0-07-020650-3.
47. Feynman, R. P.: Slow Electrons in a Polar Crystal. Phys. Rev. 97, 660 (1955).
48. Ornstein, L. S., Zernike, F.: Proc. Acad. Sci. Amst. 17, 793 (1914).
49. Ornstein, L. S., Zernike, F.: Proc. Acad. Sci. Amst. 18, 1520 (1916).
50. Ginzburg, V. L., Landau, L. D.: J. Exp. Theor. Phys. 20, 1064 (1950).
51. Abrikosov, A. A.: On the magnetic properties of superconductors of the second group. Sov. Phys. JETP 5, 1174 (1957).
52. Landau, L. D.: J. Exp. Theor. Phys. 5, 71 (1941).
53. Green, M. S., Sengers, J. V. (eds.): Critical Phenomena. Proceedings of a Conference Held in Washington, D. C., April 1965, United States Department of Commerce, National Bureau of Standards (1965).
54. Fisher, M. E.: The theory of equilibrium critical phenomena. Rep. Prog. Phys. XXX(II), 615 (1967).
55. Heller, P.: Experimental investigations of critical phenomena. Rep. Prog. Phys. XXX(II), 731 (1967).
56. Patashinskii, A. Z., Pokrovskii, V. L.: Sov. Phys. JETP 19, 667 (1964).
57. Widom, B.: J. Chem. Phys. 43, 3892 (1965).
58. Widom, B.: J. Chem. Phys. 43, 3896 (1965).
59. Patashinskii, A. Z., Pokrovskii, V. L.: Fluctuation Theory of Phase Transitions. Elsevier, Amsterdam (1979).
60. Kadanoff, L.: Physics 2, 263 (1966).
61. Stueckelberg, E. C. G., Peterman, A.: Helv. Phys. Acta 26, 499 (1953).
62. Gell-Mann, M., Low, F. E.: Phys. Rev. 95, 1300 (1954).
63. Wilson, K. G.: Phys. Rev. B 4, 3174 (1971).
64. Wilson, K. G.: Phys. Rev. B 4, 3184 (1971).
65. Cao, T. Y. (ed.): Conceptual Foundations of Quantum Field Theory. Cambridge University Press, Cambridge (1999).
66. Rukeyser, M.: Willard Gibbs: American Genius. Ox Bow Press, Woodbridge (1942). ISBN 0918024579.