Methodology of Analytic and Computational Studies on Quantum Systems

Journal of Statistical Physics

Volumn 110, Issue 3-6, 2003, Pages 945-956

  Suzuki, Masuo ^a  

^a TOKYO UNIVERSITY OF SCIENCE   (Japan)

Author keywords

Finite range interactions; Quantum transfermatrix method; ST transformation

Indexed keywords

EID: 0037276471     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022128423037     Document Type: Conference Paper

References (73)

1. M. Suzuki, J. Phys. Soc. Jpn. 21:2274 (1966). See also H. F. Trotter, Proc. Amer. Math. Soc. 10:545 (1959).
2. M. Suzuki, J. Phys. Soc. Jpn. 21:2274 (1966). See also H. F. Trotter, Proc. Amer. Math. Soc. 10:545 (1959).
3. M. Suzuki, Comm. Math. Phys. 51:183 (1976).
4. M. Suzuki, Prog. Theor. Phys. 56:1454 (1976).
5. M. Suzuki, suggested in the symposium on computer experiments held on the 11th day of October, 1983, at Okayama University.
6. M. Suzuki, Phys. Rev. B 31:2957 (1985).
7. M. Suzuki and M. Inoue, Prog. Theor. Phys. 78:787 (1987).
8. M. Inoue and M. Suzuki, Prog. Theor. Phys. 79:645 (1988).
9. M. Suzuki, S. Miyashita, and A. Kuroda, Prog. Theor. Phys. 58:1377 (1977).
10. M. Suzuki, J. Stat. Phys. 43:883 (1986).
11. M. Suzuki (ed.), Quantum Monte Carlo Methods in Condensed Matter Physics (World Scientific, Singapore, 1993).
12. H. Betsuyaku, Prog. Theor. Phys. 73:319 (1985); 75:774-808 (1986).
13. H. Betsuyaku, Prog. Theor. Phys. 73:319 (1985); 75:774-808 (1986).
14. T. Tsuzuki, Prog. Theor. Phys. 73:1352 (1985).
15. H. Betsyaku and T. Yokota, Prog. Theor. Phys. 75:808 (1986).
16. K. Kubo and Takada, J. Phys. Soc. Jpn. 55:438 (1986).
17. T. Koma, Prog. Theor. Phys. 71:269 (1993).
18. K. Kubo, Phys. Rev. B 46:866 (1992).
19. T. Delica, K. Kopinga, H. Leschke, and K. K. Mon, Europhys. Lett. 15:55 (1991).
20. N. Hatano and M. Suzuki, Prog. Theor. Phys. 85:481 (1991).
21. M. Suzuki, J. Stat. Phys. 49:977 (1987).
22. H. Umezawa, H. Matsumoto, and M. Tachiki, Thermo Field Dynamics and condensed States (North-Holland, Amsterdam, 1982) and references cited therein.
23. M. Suzuki, J. Phys. Soc. Jpn. 54:4483 (1985).
24. M. Suzuki, Phys. Lett. 111A:440 (1985).
25. O. Bratteli and D. W. Robinson, Operator Algebra and Quantum Statistical Mechanics (Springer, 1979).
26. M. E. Fisher, Rept. Prog. Phys. 30:615 (1968).
27. C. Domb and M. S. Green (eds.), Phase Transitions and Critical Phenomena, Vol. 1-6 (Academic Press, 1972-76); C. Domb and J. L. Lebowitz (eds.), Vol. 7 (1983).
28. C. Domb and M. S. Green (eds.), Phase Transitions and Critical Phenomena, Vol. 1-6 (Academic Press, 1972-76); C. Domb and J. L. Lebowitz (eds.), Vol. 7 (1983).
29. D. I. Uzunov, Introduction to the Theory of Critical Phenomena - Mean-field, Fluctuations and Renormalization (World Scientific, 1993).
30. M. Suzuki, X. Hu, M. Katori, A. Lipowski, N. Hatano, K. Minami, and Y. Nonomura, Coherent Anomaly Method Mean Field, Fluctuations and Systematics (World Scientific, 1995).
31. M. Suzuki, Phys. Lett. A 146:319 (1990); 165:387 (1992).
32. M. Suzuki, X. Hu, M. Katori, A. Lipowski, N. Hatano, K. Minami, and Y. Nonomura, Coherent Anomaly Method Mean Field, Fluctuations and Systematics (World Scientific, 1995).
33. M. Suzuki, J. Math. Phys. 32:400 (1991).
34. M. Suzuki, J. Phys. Soc. Jpn. 61:3015 (1992).
35. M. Suzuki, Physica A 191:501 (1992).
36. M. Suzuki and T. Yamauchi, J. Math. Phys. 34:4892 (1993).
37. M. Suzuki, Proc. Jpn. Acad. Ser. B 69:161 (1993).
38. M. Suzuki, Comm. Math. Phys. 163:491 (1994).
39. M. Suzuki, Physica A 205:65 (1994); and references therein.
40. H. Yoshida, Phys. Lett. A 150:262 (1990).
41. H. deRaedt and K. Michielsen, Comput. Phys. 8:600 (1994); Ann. Physik 4:679 (1995).
42. H. deRaedt and K. Michielsen, Comput. Phys. 8:600 (1994); Ann. Physik 4:679 (1995).
43. M. Suzuki, Comm. Math. Phys. 183:339 (1997).
44. M. Suzuki, J. Math. Phys. 38:1183 (1997).
45. M. Suzuki, Phys. Lett. A 224:337 (1997).
46. There are about two hundred references on the applications, which will be listed elsewhere.
47. The idea of thermo quantum dynamics was briefly reported at the conference on "Trends in Infinite Dimensional Analysis and Quantum Probability" in Kyoto, on the 20th of November, 2001.
48. H. A. Kramers and G. H. Wannier, Phys. Rev. 60:252 (1941).
49. R. Kubo, Busseiron Kenkyu 1:1 (1943).
50. E. W. Montroll, J. Chem. Phys. 9:706 (1941); 10:61 (1942).
51. E. W. Montroll, J. Chem. Phys. 9:706 (1941); 10:61 (1942).
52. E. N. Lassettre and J. P. Howe, J. Chem. Phys. 9:747 (1941).
53. L. Onsager, Phys. Rev. 65:117 (1944).
54. J. Suzuki, Y. Akutsu, and M. Wadati, J. Phys. Soc. Jpn. 59:2667 (1990).
55. J. Suzuki, T. Nagao, and M. Wadati, Int. J. Mod. Phys. B 6:1119-1180 (1992).
56. C. Destri and H. J. de Vega, Phys. Rev. Lett. 69:2313 (1992); Nuclear Phys. B 504:[PS] 621 (1997). Their argument on the exponential degeneracy of the transfer matrix is confusing.
57. C. Destri and H. J. de Vega, Phys. Rev. Lett. 69:2313 (1992); Nuclear Phys. B 504:[PS] 621 (1997). Their argument on the exponential degeneracy of the transfer matrix is confusing.
58. M. Takahashi, Phys. Rev. B 43:5788 (1991).
59. H. Mizuta, T. Nagao, and M. Wadati, J. Phys. Soc. Jpn. 63:3951 (1994).
60. A. Klümper, Z. Phys. B 91:507 (1993).
61. A. Klümper, Eur. Phys. J. B 5:677 (1998).
62. G. Jüttner and A. Klümper, Euro. Phys. Lett. 37:335 (1997).
63. G. Jüttner, A. Klümper, and J. Suzuki, Nucl. Phys. B 487:650 (1997).
64. G. Jüttner, A. Klümper, and J. Suzuki, J. Phys. A 30:1881 (1997).
65. A. Kuniba, T. Nakanishi, and J. Suzuki, Int. J. Mod. Phys. A 9:5215 (1994).
66. A. Kuniba, K. Sakai, and J. Suzuki, Nucl. Phys. B 525:[FS] 597 (1998).
67. Y. Umeno, J. Phys. Soc. Jpn. 70:2531 (2001), and references cited therein.
68. R. Blinc, J. Phys. Chem. Solids 13:204 (1960).
69. P. G. de Gennes, Solid State Comm. 1:1963 (1963).
70. S. Katsura, Phys. Rev. 127:1508 (1962).
71. P. Pfeuty, Ann. Phys. 57:79 (1970).
72. B. K. Chakrabarti, A. Dutta, and P. Sen, Quantum Ising Phases and Transitions in Transverse Ising Models, and references cited therein.
73. H. Araki, Commun. math. Phys. 14:120 (1969).