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Progress of Theoretical Physics

One-Dimensional Heisenberg Model at Finite Temperature

Minoru Takahashi

Published Aug 1, 1971• 473 citations
Publisher

Abstract

A set of integral equations which describes the thermodynamic properties of one-dimensional Heisenberg model is obtained. From these equations one can calculate the energy, entropy and magnetization of the system at given temperature and magnetic field. We have succeeded in reproducing the known exact results in the limiting cases of zero temperature, infinite temperature and infinite magnetic field.

DOI
10.1143/ptp.46.401

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A set of integral equations which describes the thermodynamic properties of one-dimensional Heisenberg model is obtained. From these equations one can calculate the energy, entropy and magnetization of the system at given temperature and magnetic field. We have succeeded in reproducing the known exact results in the limiting cases of zero temperature, infinite temperature and infinite magnetic field.
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The eigen-functions and eigen-values of finite three-dimensional Heisenberg models with anisotropy constant as a parameter (spin=1/2) were obtained exactly with the aid of group theoretical technique and by using a high speed computer. The calculated eigenvalues are identical with those obtained by Serber and Dresselhaus for the isotropic simple cubic 2×2×2 lattice. However, it was found that some terms in their full expressions were to be corrected. The zeros of the partition function of the above 2×2×2 lattice have been investigated as functions of the anisotropy parameter both in the complex temperature plane and in the complex magnetic field plane. Thermodynamic functions such as energy, specific heat, magnetization, and susceptibility have been numerically computed for these finite system.
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