One-Dimensional Anisotropic Heisenberg Model at Finite Temperatures
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概要
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The thermodynamics of the one-dimensional Heisenberg-Ising model for |Δ| <1 as well as of the X-Y-Z model is reduced to a set of non-linear integral equations under some plausible assumptions. It is remarkable that the number of unknown functions involved in them becomes finite when π/cos^<-1>Δ is a rational number for the Heisenberg-Ising model and when K_l/ζ is a rational number for the X-Y-Z model (where coupling constants J_x, J_y, and J_z are parametrized by ζ, l, and J_z as J_x=J_zcn(2ζ,l) and J_y=J_zdn(2ζ,l) ; 1-^^>l-^^>0, K_l-^^>2ζ-^^>0, and K_l is the complete elliptic integral of the first kind of modulus l). The validity of our theory has been confirmed by the high-temperature expansion of the free energy through the second term for a general value of Δ and through the fourth term for Δ=1/2.
- 理論物理学刊行会の論文
- 1972-12-25
著者
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Takahashi Minoru
Department Of Applied Physics Faculty Of Engineering Tohoku University
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SUZUKI Masuo
Institute for Solid State Physics University of Tokyo
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Takahashi Minoru
Department Of Appied Physics Tohoku University
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SUZUKI Masuo
Institute for Solid State Physics, University of Tokyo
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