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Prog. Theor. Phys. Vol. 41 No. 6 (1969) pp. 1438-1449
On the Distribution of Zeros for the Heisenberg Model
Masuo Suzuki
Institute for Solid State Physics, University of Tokyo, Minato-ku, Tokyo
(Received January 27, 1969)
Abstract:
The distribution of energy eigenvalues is discussed in the Heisenberg model. In particular, the first and second moments of energy eigenvalues are formulated. A method to reduce the partition function of the Heisenberg model with higher spin to that of spin ½ is presented. It yields the theorem which states if all the zeros of the partition function in the case of spin ½ are on the unit circle of the complex magnetic field plane, then it is true in the case of general spin. Furthermore, it is proved at low temperature that the zeros of the partition function of the ferromagnetic Heisenberg model with spin ½ are on the unit circle of the complex field plane. A theorem is given also on the distribution of zeros in antiferromagnetic case. Finally, an idea of coarse-graining of energy eigenvalues is proposed on the complex temperature plane in the Heisenberg model.
URL :
http://ptp.ipap.jp/link?PTP/41/1438/
DOI : 10.1143/PTP.41.1438
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Citing Article(s) :
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Progress of Theoretical Physics Vol. 42 No. 5 (1969) pp. 1086-1097
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Long-Range Order in Ideal Ferromagnets
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Masuo Suzuki
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Progress of Theoretical Physics Vol. 46 No. 4 (1971) pp. 1054-1070
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Scaling with a Parameter in Spin Systems near the Critical Point. I
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Masuo Suzuki
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Progress of Theoretical Physics Vol. 56 No. 5 (1976) pp. 1454-1469
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Relationship between d-Dimensional Quantal Spin Systems and (d+1)-Dimensional Ising Systems
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Masuo Suzuki
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Progress of Theoretical Physics Vol. 64 No. 3 (1980) pp. 770-781
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Symmetry Properties of the Ring Heisenberg Hamiltonian and New Sum Rule for Its Energy Eigenvalues
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Katsuhiko Fujii
