---

Prog. Theor. Phys. Supplement No.115 (1994) pp. 27-39

Formal Structure of the Cluster Variation Method

Tohru Morita

Department of Engineering Science, Faculty of Engineering, Tohoku University, Sendai 980

(Received May 11, 1992)

Abstract:

A review is given of the formulations of the cluster variation method, focusing on the formal structure. We consider the variational method and the method of consistencies in statistical mechanics. Comparisons are made of formulations of the cluster variation method in the variational method. In the final part, a derivation is given of the equations in the corresponding formulation in the method of consistencies.

URL : http://ptp.ipap.jp/link?PTPS/115/27/
DOI : 10.1143/PTPS.115.27

[ Full Text PDF : FREE ACCESS (864K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

---

References:

1. R. Fowler and E. A. Guggenheim, Statistical Thermodynamics, 2nd ed. (Cambridge U. P., 1952), chap. XIII.
2. H. A. Bethe, Proc. R. Soc. London A 150 (1935), 552.
3. H. A. Kramers and G. H. Wannier, Phys. Rev. 60 (1941), 252[APS]; ibid. 60 (1941), 263[APS].
4. L. Onsager, Phys. Rev. 65 (1944), 117[APS].
5. G. H. Wannier, Rev. Mod. Phys. 17 (1945), 50[APS].
6. R. Kikuchi, Phys. Rev. 81 (1951), 988[APS].
7. M. Kurata, R. Kikuchi and T. Watari, J. Chem. Phys. 21 (1953), 434[CrossRef].
8. M. Suzuki, J. Phys. Soc. Jpn. 55 (1986), 4205[JPSJ].
9. M. Katori and M. Suzuki, J. Phys. Soc. Jpn. 57 (1988), 3753[JPSJ].
   S. Fujiki, Proc. YKIS'88, Cooperative Dynamics in Complex Physical Systems, Kyoto 1988 (Springer-Verlag, Berlin, 1989), p. 179.
   S. Fujiki, M. Katori and M. Suzuki, J. Phys. Soc. Jpn. 59 (1990), 2681[JPSJ].
10. K. Wada and N. Watanabe, J. Phys. Soc. Jpn. 58 (1989), 4358[JPSJ]; ibid. 59 (1990), 2610[JPSJ].
    K. Wada, N. Watanabe and T. Uchida, J. Phys. Soc. Jpn. 60 (1991), 3289[JPSJ].
11. K. Tanaka, T. Horiguchi and T. Morita, J. Phys. Soc. Jpn. 60 (1991), 2576[JPSJ]; Phys. Lett. A 165 (1992), 266[CrossRef]; Prog. Theor. Phys. Suppl. No. 115 (1994), 221[PTP].
12. J. A. Barker, Proc. R. Soc. London A 216 (1953), 45.
13. J. Hijmans and J. de Boer, Physica 21 (1955), 471[CrossRef].
14. T. Morita, J. Phys. Soc. Jpn. 12 (1957), 753[JPSJ].
15. T. Morita, J. Math. Phys. 13 (1972), 115[CrossRef].
16. T. Morita, J. Stat. Phys. 34 (1984), 319.
17. T. Morita, J. Phys. Soc. Jpn. 12 (1957), 1060[JPSJ].
18. A. G. Schlijper, Phys. Rev. B 27 (1983), 6841[APS].
19. T. Morita, J. Stat. Phys. 59 (1990), 819.
20. T. Oguchi, Prog. Theor. Phys. 13 (1955), 148[PTP].
21. M. Suzuki, Prog. Theor. Phys. Suppl. No. 87 (1986), 1[PTP].
22. P. W. Kasteleijn and J. Van Kranendonk, Physica 22 (1956), 317[CrossRef].
    P. W. Kasteleijn, Physica 22 (1956), 387[CrossRef].
23. J. G. Kirkwood, J. Chem. Phys. 18 (1950), 380[CrossRef].
24. T. Morita, Prog. Theor. Phys. 85 (1991), 243[PTP].
25. R. A. Farrell, T. Morita and P. H. E. Meijer, J. Chem. Phys. 45 (1966), 349[AIP Scitation].
26. Y. Takagi, Proc. Math.-Phys. Soc. Jpn. 23 (1941), 44.
27. G.-C. Rota, Z. Wahrsch. 2 (1964), 340.
28. G. An, J. Stat. Phys. 52 (1988), 727.
29. T. Morita, Phys. Lett. A 161 (1991), 140[CrossRef].
30. T. Morita, Physica A 155 (1989), 73[CrossRef].

Citing Article(s) :

1. Journal of the Physical Society of Japan 63 (1994) pp. 2909-2918 :

   Application of Cluster Variation Method to Three-Dimensional t-J Model

   Kazuyuki Tanaka, Yositake Takane, Hiromichi Ebisawa and Tohru Morita

2. Progress of Theoretical Physics Vol. 92 No. 6 (1994) pp. 1081-1093 :

   An Approximation Scheme of the Cluster Variation Method for Quantum Lattice Gases

   Tohru Morita

---

[PTP HOME] [BROWSE] [SEARCH] [SUBSCRIPTION] [SUBMISSION] [REGISTRATION]

Copyright © Progress of Theoretical Physics 2013 All rights reserved.