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American Journal of Physics

Magnetism in One-Dimensional Systems—The Heisenberg Model for Infinite Spin

Michael Ellis Fisher

Published May 1, 1964• 1,544 citations
Publisher

Abstract

It is observed that the free-energy, susceptibility, and correlation functions for a linear chain of N spins with nearest-neighbor isotropic Heisenberg coupling can be calculated explicitly in the (classical) limit of infinite spin. The results are compared briefly with those for Ising and Heisenberg chains of spin 12.
DOI
10.1119/1.1970340

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The specific heat, the susceptibility, and the correlation function at zero field above the critical temperature of the random mixture (quenched site and bond problems) of the classical Heisenberg spins with nearest neighbor interaction were obtained exactly for the linear chain and for an infinite Bethe lattice (Bethe approximation of the two and three dimensional lattices) above the critical temperature. The results are simply expressed by the replacements of 2 cosh K → 4π (sinh K)/K and tanh K → L(K) (L(K) = Langevin function) for K = KAA, KAB, KBA, and KBB in the corresponding expressions of the random mixture of the Ising spins, and qualitative properties of both models are similar.
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