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Prog. Theor. Phys. Vol. 84 No. 3 (1990) pp. 410-414
Asymptotic Forms of Some Block Toeplitz Determinants
Kazuyuki Tanaka and
Tohru Morita
Department of Engineering Science, Faculty of Engineering,
Tohoku University, Sendai 980
(Received April 18, 1990)
Abstract:
A block Toeplitz determinant which expresses the spin pair correlation function of the Ising model on some two-dimensional lattices is expressed by a modified Toeplitz determinant with a simpler generating function. We show that an application of the theory developed for the modified block Toeplitz determinant readily provides the asymptotic behaviors of the block Toeplitz determinant.
URL :
http://ptp.ipap.jp/link?PTP/84/410/
DOI : 10.1143/PTP.84.410
References:
- T. Morita, Prog. Theor. Phys. 83 (1990), 701[PTP].
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H. Au-Yang and B. M. McCoy, Phys. Rev. B10 (1974), 886[APS].
- K. Tanaka, T. Morita and K. Hiroike, Prog. Theor. Phys. 84 (1990), 392[PTP].
- K. Tanaka and T. Morita, in preparation.
- G. Szegö, Commun. Seminair Math. Univ. Lund. dédié à Marcel Riesz (1952), 228.
I. I. Hirshman, Jr., J. Anal. Math. 14 (1965), 225; Journal of Mathematical Analysis and Applications 11 (1965), 290.
A. Devinatz, Illinois J. Math. 11 (1967), 160.
T. Morita, J. Math. Phys., to be published.
Citing Article(s) :
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Progress of Theoretical Physics Vol. 84 No. 3 (1990) pp. 392-409
:
-
Asymptotic Behaviors of Modified Block Toeplitz Determinant
-
Kazuyuki Tanaka and Tohru Morita
-
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
