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A new method for calculation of the magnetic properties in one- and two-dimensional spin systems with anisotropic Heisenberg exchange

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  • Tanaka, Yoshiaki
  • Uryŭ, Norikiyo

Abstract

A new approximation method is proposed for the calculation of the magnetic susceptibility of one-dimensional assembly of spins and the critical temperature of two-dimensional one both with the anisotropic Heisenberg exchange. In a linear chain system, every spins are grouped into pairs of adjacent spins (pair-approximation) or clusters of adjacent three spins ((q+1)-approximation), and the partition function of the total spin system is approximated as a sum of products of the partitions functions for the pairs or the clusters. Then the partition function of the anisotropic Heisenberg spin system is shown to reduce into a form of the Ising spin system with modified coupling constants. The exact result for the Ising chain system enables us to obtain an analytical expression for the magnetic susceptibility of anisotropic Heisenberg chain system. The same approximations are also applied to two-dimensional lattices, and the critical temperatures of the square, triangular, and honeycomb lattices with anisotropic Heisenberg exchange are calculated as a function of anisotropy parameter. The results are compared with those of the existing theories and shown to be quite excellent.

Suggested Citation

  • Tanaka, Yoshiaki & Uryŭ, Norikiyo, 1981. "A new method for calculation of the magnetic properties in one- and two-dimensional spin systems with anisotropic Heisenberg exchange," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 105(3), pages 493-516.
    • Handle: RePEc:eee:phsmap:v:105:y:1981:i:3:p:493-516
    DOI: 10.1016/0378-4371(81)90107-2
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    References listed on IDEAS

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    1. Storing, Herbert J. & Strauss, Leo & Berns, Walter & Storing, Herbert J. & Weinstein, Leo & Horwitz, Robert, 1963. "Replies to Schaar and Wolin: I," American Political Science Review, Cambridge University Press, vol. 57(1), pages 151-160, March.
    2. Kuryuzawa, Takeo & Курюдзава, Такэо, 1980. "ロシア中世都市における手工業と手工業者 (I) = К Вопросу О Ремесле И Ремесленниках В Древнерусском Городе (I)," 商学討究 (Shogaku Tokyu), Otaru University of Commerce, vol. 31(1), pages 40-66.
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