Abstract

The coupled transcendental equations of Bethe, which determine eigen-values of the one-dimensional Heisenberg model, are decomposed into uncoupled equations in the case of two reversed spins. The second cluster integral which determines exact behavior in the high field and low temperature region, is calculated by solving these equations. The contribution of bound states is dominant in the case of ferromagnetic interaction. Spin wave theory using Bose statistics gives the low bound of the magnetization, while Frank's and Mannari's theories using Fermi statistics give the upper bound of it in the case of ferromagnetic interaction.

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