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Prog. Theor. Phys. Vol. 58 No. 5 (1977) pp. 1377-1387

[ Full Text PDF : FREE ACCESS (874K) ]

Monte Carlo Simulation of Quantum Spin Systems. I

Masuo Suzuki, Seiji Miyashita and Akira Kuroda

Department of Physics, University of Tokyo, Tokyo 113

(Received June 9, 1977)

Abstract:

A general explicit formulation of Monte Carlo simulation for quantum systems is given in this paper on the basis of the previous fundamental proposal by Suzuki. This paper also demonstrates explicitly the possibility of it and gives new interesting physical results on the two-dimensional XY-model. That is, the present preliminary simulation seems to indicate a phase transition with a divergent susceptibility, and a very weak singularity of specific heat of it exists, and without long-range order.


URL : http://ptp.ipap.jp/link?PTP/58/1377/
DOI : 10.1143/PTP.58.1377

[ Full Text PDF : FREE ACCESS (874K) ] Citation:

References:

  1. See D. D. Betts, in Phase Transitions and Critical Phenomena, Vol. 3, edited by C. Domb and M. S. Green, (Academic Press, New York).
  2. J. M. Kosterlitz and D. J. Thouless, J. of Phys. C 6 (1973), 1181[IoP STACKS].
    J. M. Kosterlitz, J. of Phys. C 7 (1974), 1046[IoP STACKS].
  3. V. L. Berezinskii, Sov. Phys. -JETP 32 (1971), 493; ibid. 34 (1972), 610; ibid. 37 (1973), 369.
  4. J. Zittartz, Z. Phys. B 23 (1976), 55; ibid. 23 (1976), 63.
  5. H. J. Mikeska and H. Schmidt, J. Low Temp. Phys. 2 (1970), 371[CrossRef].
  6. J. Villain, J. de Phys. 36 (1975), 581.
  7. J. Rogiers and R. Dekeyser, Phys. Rev. B 13 (1976), 4886[APS].
  8. J. Rogiers and D. D. Betts, Physica A 85 (1976), 553[CrossRef].
    D. D. Betts, Physica B+C 86-88 (1977), 556[CrossRef].
  9. R. C. Brower, F. Kuttner, M. Nauenberg and K. Subbarao, preprint.
  10. K. Yamaji and J. Kondo, J. Phys. Soc. Jpn. 35 (1973), 25[JPSJ].
  11. J. V. José, L. P. Kadanoff, S. Kirkpatrick and D. R. Nelson, Phys. Rev. B 16 (1977), 1217[APS].
  12. H. E. Stanley and T. A. Kaplan, Phys. Rev. Lett. 17 (1966), 913[APS].
  13. M. Suzuki, Commun. Math. Phys. 51 (1976), 183, [CrossRef]and references cited therein.
  14. M. Suzuki, Prog. Theor. Phys. 56 (1976), 1454[PTP].
  15. M. Suzuki, S. Miyashita, A. Kuroda and C. Kawabata, Phys. Lett. A 60 (1977), 478[CrossRef].
  16. M. Suzuki, Proceedings of the International Conference of Frontiers of the Theoretical Physics and Winter School, held at New Delhi, January 6-22, 1977.
  17. M. Barma and B. S. Shastry, Phys. Lett. A 61 (1977), 15[CrossRef].
  18. M. Suzuki, Prog. Theor. Phys. 58 (1977), 755[PTP].
  19. K. Binder, in Phase Transition and Critical Phenomena, Vol. 5B, edited by C. Domb and M. S. Green, (Academic Press, New York).
  20. K. Binder and D. P. Landau, Phys. Rev. B 13 (1976), 1140[APS].
  21. C. Kawabata and K. Binder, Solid State Commun. 22 (1977), 705[CrossRef].
  22. M. Suzuki, S. Miyashita and A. Kuroda, Prog. Theor. Phys. 58 (1977), 701[PTP].
  23. M. Suzuki, J. Phys. Soc. Jpn. 21 (1966), 2274[JPSJ].
  24. S. Katsura, Phys. Rev. 127 (1962), 1508[APS].
  25. E. Lieb, T. Schultz and D. Mattis, Ann. of Phys. 16 (1961), 407[CrossRef].
  26. J. C. Bonner and M. E. Fisher, Phys. Rev. A 135 (1964), 640[APS].
  27. S. F. Edwards ad P. W. Anderson, J. of Phys. F 5 (1975), 965[IoP STACKS].
  28. M. Suzuki, Prog. Theor. Phys. 58 (1977), 1151, [PTP]and references cited therein.

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  12. Journal of the Physical Society of Japan 73 (2004) pp. 1379-1414 :
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  20. Progress of Theoretical Physics Vol. 72 No. 6 (1984) pp. 1245-1247 :
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  21. Progress of Theoretical Physics Vol. 73 No. 2 (1985) pp. 319-331 :
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  23. Progress of Theoretical Physics Vol. 73 No. 3 (1985) pp. 833-836 :
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  24. Progress of Theoretical Physics Vol. 73 No. 6 (1985) pp. 1352-1368 :
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  25. Progress of Theoretical Physics Vol. 75 No. 1 (1986) pp. 46-58 :
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  26. Progress of Theoretical Physics Vol. 75 No. 2 (1986) pp. 451-454 :
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  27. Progress of Theoretical Physics Vol. 75 No. 4 (1986) pp. 774-789 :
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  28. Progress of Theoretical Physics Vol. 75 No. 4 (1986) pp. 808-827 :
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  29. Progress of Theoretical Physics Vol. 75 No. 5 (1986) pp. 1058-1065 :
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  30. Progress of Theoretical Physics Vol. 75 No. 5 (1986) pp. 1254-1257 :
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  32. Progress of Theoretical Physics Vol. 78 No. 2 (1987) pp. 224-236 :
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  33. Progress of Theoretical Physics Vol. 78 No. 4 (1987) pp. 787-799 :
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  36. Progress of Theoretical Physics Supplement No.80 (1984) pp. 146-155 :
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