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Prog. Theor. Phys. Vol. 51 No. 1 (1974) pp. 82-98

Bethe Lattice and the Bethe Approximation

Shigetoshi Katsura and Makoto Takizawa

Department of Applied Physics, Tohoku University, Sendai

(Received July 2, 1973)

Abstract:

Statistical mechanics of the Bethe lattice was developed. Properties of the Bethe lattice, i. e., (of the Bethe approximation) were summarized including low temperature susceptibilities of ferro- and antiferromagnets. The equivalence of the exact solution of the Bethe lattice to the Bethe approximation of the Ising model in the case of the antiferromagnetism was shown. The partition function of the Bethe lattice with first and second neighbor interactions was obtained and the critical temperature was calculated in the case where the first neighbor interaction is ferromagnetic.

URL : http://ptp.ipap.jp/link?PTP/51/82/
DOI : 10.1143/PTP.51.82

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See Also:

• Progress of Theoretical Physics Vol. 52 No. 3 (1974) pp. 1075-1075 :

  Erratum : Bethe Lattice and the Bethe Approximation

  Shigetoshi Katsura and Makoto Takizawa

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Citing Article(s) :

1. Journal of the Physical Society of Japan 58 (1989) pp. 3642-3650 :

   Canonical Series of Exactly Solvable Models for the CAM –Spontaneous Broken Symmetry of Effective Hamiltonians Based on the Confluent Transfer-Matrix Method–

   Masuo Suzuki

2. Progress of Theoretical Physics Vol. 51 No. 4 (1974) pp. 1053-1063 :

   Infinite Susceptibility without Spontaneous Magnetization

   Hirotsugu Matsuda

3. Progress of Theoretical Physics Vol. 52 No. 6 (1974) pp. 1798-1806 :

   Percolation Theory and the Ising Model for a Class of Triangular Cactii

   A. R. Bishop

4. Progress of Theoretical Physics Vol. 53 No. 5 (1975) pp. 1337-1347 :

   The Ising Model on the Cayley Trees

   Takashi Tsuchiya and Nobuhiko Saitô

5. Progress of Theoretical Physics Vol. 54 No. 4 (1975) pp. 982-998 :

   Susceptibility and Correlation Function of the Ising Model on the Cayley Tree

   Tohru Morita and Tsuyoshi Horiguchi

6. Progress of Theoretical Physics Vol. 54 No. 4 (1975) pp. 1028-1038 :

   The Heisenberg Model on the Cayley Tree

   Tohru Ogawa

7. Progress of Theoretical Physics Vol. 54 No. 4 (1975) pp. 1067-1076 :

   Temperature-Dependent Percolation Problem in the Bethe Lattice

   Takashi Odagaki

8. Progress of Theoretical Physics Vol. 55 No. 1 (1976) pp. 81-89 :

   Magnetization of Each Site in Ising Model under Weak Field on the Cayley Tree

   Shunichi Muto and Takehiko Oguchi

9. Progress of Theoretical Physics Vol. 55 No. 4 (1976) pp. 1049-1063 :

   Random Mixture of the Ising Magnets in a Magnetic Field

   Shigetoshi Katsura

10. Progress of Theoretical Physics Vol. 55 No. 4 (1976) pp. 1298-1299 :

    Linear and Nonlinear Critical Slowing Down in the Kinetic Ising Model

    Hiroshi Ikeda

11. Progress of Theoretical Physics Vol. 56 No. 2 (1976) pp. 435-449 :

    A Method of Determining the Orderings of the Ising Model with Several Neighbor Interactions under the Magnetic Field and Applications to Hexagonal Lattices

    Tomoshige Kudō and Shigetoshi Katsura

12. Progress of Theoretical Physics Vol. 58 No. 2 (1977) pp. 434-451 :

    Susceptibility and Specific Heat in the Glass-Like Phase

    Shigetoshi Katsura

13. Progress of Theoretical Physics Vol. 59 No. 4 (1978) pp. 1101-1115 :

    Lattice Vibration of the Cayley Tree

    Koh Wada, Takehiko Fujita and Takashi Asahi

14. Progress of Theoretical Physics Vol. 65 No. 4 (1981) pp. 1130-1144 :

    Nonlinear Susceptibility in the Spin Glass

    Sumiyoshi Fujiki and Shigetoshi Katsura

15. Progress of Theoretical Physics Supplement No.87 (1986) pp. 139-154 :

    Theory of Spin Glass by the Method of the Distribution Function of an Effective Field

    Shigetoshi Katsura

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