HOME    |    BROWSE    |    SEARCH    |    SUBSCRIPTION   |    SUBMISSION    |    REGISTRATION

Quick Search:
Author: Title/Abstract: Vol./No: Page:
PTP Online Top > Volume 98 (1997) > Number 1
| Next Article >

Prog. Theor. Phys. Vol. 98 No. 1 (1997) pp. 39-55

[ Full Text PDF : FREE ACCESS (846K) ]

Annealed Character of Spin Clusters in Ising Spin Systems

Yasuhiro Kasai, Hitoshi Imaoka and Kohzaburo Ohnaka

School of Applied Physics, Osaka University, Suita 565

(Received September 30, 1996)

Abstract:

An arbitrary Ising spin system can be expressed by a bond percolation system of spin clusters through the Kasteleyn-Fortuin transformation. The generating function of the percolation system with temperature and internal-freedom related variables can be expressed as the Legendre transformation of the entropy, where conjugate topological variables are the numbers of bonds and clusters in the respective cases. The percolation system has an annealed character whose bond configuration changes in the thermodynamic process. Even for a 2D strongly frustrated Ising system, at a finite temperature there exists a percolation transition which is a real singular point of the entropy. The annealed character determines the universality class as that of the ferromagnetic Potts model with one degree of internal freedom (random percolation). The reduced freedom hides the strong order in the generating function.


URL : http://ptp.ipap.jp/link?PTP/98/39/
DOI : 10.1143/PTP.98.39

[ Full Text PDF : FREE ACCESS (846K) ] Citation:

References:

  1. P. W. Kasteleyn and C. M. Fortuin, J. Phys. Soc. Jpn. Suppl. 26 (1969), 11.
  2. C. M. Fortuin and P. W. Kasteleyn, Physica 57 (1972), 536[CrossRef].
  3. C. -K. Hu, Phys. Rev. B29 (1984), 5103[APS].
  4. Y. Kasai and A. Okiji, Prog. Theor. Phys. 79 (1988), 1080[PTP].
  5. A. Coniglio, F. di Liberto, G. Monroy and F. Peruggi, Phys. Rev. B44 (1991), 12605[APS].
  6. I. Syozi, Prog. Theor. Phys. 34 (1965), 189[PTP].
    I. Syozi, Phase Transitions and Critical Phenomena 1, ed. C. Domb and M. S. Green (Academic, London 1972), p. 269.
    J. W. Essam and H. Garelick, Proc. Phys. Soc. 92 (1967), 136.
  7. M. E. Fisher, Phys. Rev. 176 (1968), 257[APS].
  8. M. Suzuki, Prog. Theor. Phys. 51 (1974), 1992[PTP].
  9. Y. Kasai, Proc. Int. Conf.eCoherent Approach to Fluctuations' ed. M. Suzuki and
    N. Kawashima (World Scientific, 1996), 184.
  10. Y. Kasai and K. Ohnaka, Prog. Theor. Phys. 82 (1989), 1057[PTP].
    Y. Kasai and K. Ohnaka, Proc. Int. Conf.eMagnetic Phase Transition' ; J. Magn. Magn. Mater. 90-91 (1990), 291.
    H. Imaoka and Y. Kasai, J. Phys. Soc. Jpn. 65 (1996), 725[JPSJ].
  11. V. Cataudella, Physica A183 (1992), 249.
    The coincidence is suggested in L. de Arcangelis, A. Coniglio and F. Peruggi, Europhys. Lett. 14 (1991), 515[CrossRef].
  12. G. -M. Zhang and C. -Z. Yang, Europhys. Lett. 22 (1993), 505.
  13. S. Parakash, A. Coniglio and E. Stanley, Phys. Rev. E49 (1994), 2747[APS].
  14. G. H. Wannier, Phys. Rev. 79 (1950), 357[APS].
    R. M. F. Houtappel, Physica 16 (1950), 425[CrossRef].
    I. Syozi, Prog. Theor. Phys. 6 (1951), 306[PTP].
    I. Syozi and H. Nakano, Prog. Theor. Phys. 13 (1955), 69[PTP].
    V. G. Vaks, A. I. Larkin and Y. N. Ovchinnikov, Sov. Phys. -JETP 22 (1966), 1180.
    Y. Kasai, Prog. Theor. Phys. 57 (1977), 1497[PTP].
    G. Andre, R. Bidaux, J. -P. Carton, R. Conte and L. de Seze, J. de Phys. 40 (1979), 479.
    R. Liebmann, Lecture Notes in Phys. 251 Statistical Mechanics of Periodic Frustrated Ising Systems (Springer, Berlin,1986).
  15. V. Cataudella, A. Coniglio, L. de Arcangelis and F.di Liberto, Physica A192 (1993), 167.
  16. A. U. Neumann and B. Derrida, J. de Phys. 49 (1988), 1647.
    A. M. Maritz, H. J. Herrmann and L. de Arcangelis, J. Stat. Phys. 59 (1990), 1043.
  17. D. H. Swendsen and J. -S. Wang, Phys. Rev. B38 (1988), 4840[APS].
  18. D. Kandel, R. Ben-Av and E. Domany, Phys. Rev. Lett. 65 (1990), 65[APS].
  19. M. Suzuki, Prog. Theor. Phys. 58 (1977), 1151[PTP].
    Y. Kasai, A. Okiji and I. Syozi, Prog. Theor. Phys. 65 (1981), 140[PTP].
  20. Y. Kasai and A. Okiji, Prog. Theor. Phys. 69 (1983), 20[PTP].
  21. R. H. Swendsen and J. -S. Wang, Phys. Rev. Lett. 58 (1987), 86[APS].
  22. D. Kandel, R. Ben-Av and E. Domany, Phys. Rev. B45 (1992), 4700[APS].
  23. G. M. Zhang and C. Z. Yang, Phys. Rev. B50 (1994), 12546[APS].

Citing Article(s) :

  1. Journal of the Physical Society of Japan 67 (1998) pp. 2300-2305 :
    Explicit KF-Percolation Transitions in 2D Strongly-Frustrated Spin Systems
    Hideo Ikeda and Yasuhiro Kasai
  2. Journal of the Physical Society of Japan 71 (2002) pp. 2669-2676 :
    Setup of Frustration in Potts Spin Systems
    Yasuhiro Kasai

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

Copyright © Progress of Theoretical Physics 2013 All rights reserved.