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Prog. Theor. Phys. Vol. 75 No. 5 (1986) pp. 1254-1257

[ Full Text PDF : FREE ACCESS (235K) ]

Letters

Monte Carlo Simulation of Quantum Heisenberg Magnets on the Triangular Lattice

Masako Takasu, Seiji Miyashita and Masuo Suzuki

Department of Physics, University of Tokyo, Tokyo 113

(Received February 12, 1986)

Abstract:

Quantum Heisenberg spin systems (S=1/2) have been studied by quantum Monte Carlo method based on the equivalence theorem of Suzuki. Thermodynamic properties are investigated for ferromagnetic and antiferromagnetic models on the triangular lattice. The difficulty in Monte Carlo simulation due to the negative sign of transition probability is also discussed.


URL : http://ptp.ipap.jp/link?PTP/75/1254/
DOI : 10.1143/PTP.75.1254

[ Full Text PDF : FREE ACCESS (235K) ] Citation:

References:

  1. K. Binder, ed. Monte Carlo Methods in Statistical Physics (Springer, Berlin, 1979); Application of the Monte Carlo Methods in Statistical Physics (Springer, Berlin, 1984).
  2. M. Suzuki, Commun. Math. Phys. 51 (1976), 183[CrossRef]; ibid. 57 (1977), 193[CrossRef]; Prog. Theor. Phys. 56 (1976), 1454[PTP]; J. Math. Phys. 26 (1985), 601[CrossRef]; Phys. Rev. B31 (1985), 2975[APS]; J. Stat. Phys. 43 (1986), 883.
  3. M. Suzuki, S. Miyashita and A. Kuroda, Prog. Theor. Phys. 58 (1977), 1377[PTP].
    See also H. De. Raedt and A. Lagendijk, Phys. Rep. 127 (1985), 233, [CrossRef]and references therein.
  4. P. W. Anderson, Mater. Res. Bull. 8 (1973), 153.
    P. Fazekas and P. W. Anderson, Philos. Mag. 30 (1974), 423.
  5. D. D. Betts and J. Oitmaa, Phys. Lett. 62A (1977), 277.
    J. Oitmaa and D. D. Betts, Can. J. Phys. 56 (1978), 897.
  6. L. G. Marland and D. D. Betts, Phys. Rev. Lett. 43 (1979), 1618[APS].
    T. Oguchi, H. Nishimori and Y. Taguchi, J. Phys. Soc. Jpn. 55 (1986), 323[JPSJ].
    S. Fujiki and D. D. Betts, Can. J. Phys. (in press).
  7. S. Miyashita, J. Phys. Soc. Jpn. 53 (1984), 44[JPSJ].
  8. M. Suzuki, J. Stat. Phys. (1986), in press; in Progress in Quantum Field Theory, ed. H. Ezawa and S. Kamefuchi (North Holland, 1986).
    See also J. Phys. Soc. Jpn. 54 (1985), 4483[JPSJ].
  9. D. H. Lee, J. D. Joannopoulos and J. W. Negele, Phys. Rev. B30 (1984), 1599[APS].
  10. H. Nishimori, private communication.
  11. K. Hirakawa, H. Kadowaki, K. Ubukoshi, J. Phys. Soc. Jpn. 54 (1985), 3526[JPSJ].
    I. Yamada, K. Ubukoshi and K, Hirakawa, J. Phys. Soc. Jpn. 54 (1985), 3571[JPSJ].
  12. H. Kawamura and S. Miyashita, J. Phys. Soc. Jpn. 53 (1984), 4138[JPSJ].
  13. G. S. Rushbrooke, G. A. Baker, Jr. and P. J. Wood, in Phase Transitions and Critical Phenomena, ed. C. Domb and M. S. Green (Academic Press, London, 1974), vol. 3.
  14. M. Suzuki, Phys. Lett. 113A (1985), 299.
  15. M. Imada, J. Phys. Soc. Jpn. 53 (1984), 2861[JPSJ].
  16. For the quantum Villain model, the negative sign problem can be avoided for n=1 by a variable transformation. See T. Onogi, S. Miyashita and M. Suzuki, submitted to J. Stat. Phys.
  17. The dependence (4) has been pointed out in J. E. Hirsch, D. J. Scalapino, R. L. Sugar and R. Blankenbecler, Phys. Rev. B26 (1982), 5033[APS].

Citing Article(s) :

  1. Journal of the Physical Society of Japan 56 (1987) pp. 1963-1973 :
    Cluster-Spin Quantum Monte Carlo Study of One-Dimensional Heisenberg Model
    Yutaka Okabe and Macoto Kikuchi
  2. Journal of the Physical Society of Japan 56 (1987) pp. 2153-2167 :
    Ground-State Properties of the One-Dimensional Isotropic Spin-1/2 Heisenberg Antiferromagnet with Competing Interactions
    Takashi Tonegawa and Isao Harada
  3. Journal of the Physical Society of Japan 57 (1988) pp. 626-638 :
    Ground State of Quantum Spin Systems on the Triangular Lattice
    Hidetoshi Nishimori and Hiizu Nakanishi
  4. Journal of the Physical Society of Japan 57 (1988) pp. 2310-2330 :
    Statistical Mechanical Theory of Cooperative Phenomena. II. Super-Effective-Field Theory with Applications to Exotic Phase Transitions
    Masuo Suzuki
  5. Journal of the Physical Society of Japan 57 (1988) pp. 2779-2790 :
    Thermodynamic Properties of the One-Dimensional Spin-1/2 Heisenberg Antiferromagnet with Competing Interactions
    Isao Harada, Tetsuji Kimura and Takashi Tonegawa
  6. Journal of the Physical Society of Japan 57 (1988) pp. 3733-3741 :
    RVB States for Tow-Dimensional Antiferromagnets
    Makoto Inoue, Tetsuhiko Chikyu, Xiao Hu and Masuo Suzuki
  7. Journal of the Physical Society of Japan 57 (1988) pp. 4351-4358 :
    Quantum Monte Carlo Simulation of the Spin 1/2 XXZ Model on the Square Lattice
    Yutaka Okabe and Macoto Kikuchi
  8. Journal of the Physical Society of Japan 58 (1989) pp. 2650-2653 :
    Chirality and Flux in Two-Dimensional Spin-1/2 Antiferromagnets –Exact Diagonalization Study–
    Masatoshi Imada
  9. Journal of the Physical Society of Japan 60 (1991) pp. 614-624 :
    Boson Mean Field Theory of the Triangular Lattice Heisenberg Model
    Daijiro Yoshioka and Jun Miyazaki
  10. Journal of the Physical Society of Japan 61 (1992) pp. 983-988 :
    Spin-Wave Results for the Staggered Magnetization of Triangular Heisenberg Antiferromagnet
    Satoru J. Miyake
  11. Journal of the Physical Society of Japan 62 (1993) pp. 880-887 :
    Thermodynamic Properties of Antiferromagnetic Quantum XY-Model on the Triangular Lattice
    Shigeo Homma, Hirotsugu Matsuda, Naofumi Ogita and Kazuhiro Sano
  12. Journal of the Physical Society of Japan 63 (1994) pp. 1691-1697 :
    Data Analysis for Quantum Monte Carlo Simulations with the Negative-Sign Problem
    Naomichi Hatano
  13. Progress of Theoretical Physics Vol. 77 No. 2 (1987) pp. 287-296 :
    Quantum Monte Carlo Simulation of Antiferromagnetic Heisenberg Model on the Triangular Lattice
    Kazuhiro Sano
  14. Progress of Theoretical Physics Vol. 79 No. 3 (1988) pp. 645-664 :
    The ST-Transformation Approach to Analytic Solutions of Quantum Systems. II
    Makoto Inoue and Masuo Suzuki
  15. Progress of Theoretical Physics Supplement No.87 (1986) pp. 112-126 :
    The Ground State and Thermodynamic Properties of Generalized Heisenberg Models on the Triangular Lattice
    Seiji Miyashita
  16. Progress of Theoretical Physics Supplement No.87 (1986) pp. 127-138 :
    Decoupled Cell Monte Carlo Method for Quantum Spin Systems on Linear Chain and on Triangular Lattice
    Shigeo Homma, Kazuhiro Sano, Hirotsugu Matsuda and Naofumi Ogita
  17. Progress of Theoretical Physics Supplement No.87 (1986) pp. 247-255 :
    Numerical Diagonalization of Quantum Spin Hamiltonians
    Hidetoshi Nishimori and Yoshihiro Taguchi

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