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Prog. Theor. Phys. Vol. 84 No. 3 (1990) pp. 392-409

[ Full Text PDF : FREE ACCESS (695K) ]

Asymptotic Behaviors of Modified Block Toeplitz Determinant

Kazuyuki Tanaka and Tohru Morita

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

(Received April 18, 1990)

Abstract:

Some formulas are given for the asymptotic form of N ×N modified block Toeplitz determinants for large N. These formulas are useful in obtaining the asymptotic behaviors of the correlation function of two spins of the Ising model on a two-dimensional regular lattice when the two spins are not on an axis.


URL : http://ptp.ipap.jp/link?PTP/84/392/
DOI : 10.1143/PTP.84.392

[ Full Text PDF : FREE ACCESS (695K) ] Citation:

References:

  1. T. T. Wu, Phys. Rev. 149 (1966), 380[APS].
    B. M. McCoy and T. T. Wu, The Two-Dimensional Ising Model (Harvard University Press, 1973).
  2. B. M. McCoy and T. T. Wu, Phys. Rev. 155 (1967), 438[APS].
  3. H. Au-Yang and B. M. McCoy, Phys. Rev. B10 (1974), 3885[APS].
  4. W. F. Wolff and J. Zittartz, Z. Phys. B47 (1982), 341.
  5. T. Chikyu and M. Suzuki, Prog. Theor. Phys. 81 (1989), 927[PTP].
  6. T. Morita, unpublished note.
  7. K. Tanaka and T. Morita, Prog. Theor. Phys. 84 (1990), 410[PTP].
  8. I Satake, Linear Algebra (Dekker Press, 1974).
  9. I. C. Gohberg and M. G. Krein, Am. Math. Soc. Trans. 14 (1958), 217.
  10. K. Tanaka, Doctor Thesis (Tohoku University, Japan, 1989), in Japanese.
  11. K. Tanaka, T. Morita and K. Hiroike, in preparation.

Citing Article(s) :

  1. Journal of the Physical Society of Japan 61 (1992) pp. 64-69 :
    Low-Temperature Behavior of Antiferromagnetic Ising Model on Triangular Lattice
    Tsuyoshi Horiguchi, Kazuyuki Tanaka and Tohru Morita
  2. Progress of Theoretical Physics Vol. 84 No. 3 (1990) pp. 410-414 :
    Asymptotic Forms of Some Block Toeplitz Determinants
    Kazuyuki Tanaka and Tohru Morita
  3. Progress of Theoretical Physics Vol. 88 No. 5 (1992) pp. 865-880 :
    Asymptotic Behavior of Spin-Pair Correlation Function of Ising Model on Checkerboard Lattice
    Kazuyuki Tanaka and Tohru Morita

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