Abstract
The anisotropic Hamiltonian, of the linear spin array in the Heisenberg model of magnetism is examined. The eigenstate and the partition function for the case are obtained exactly for a finite system and for an infinite system with the aid of annihilation and creation operators, and the free energy of the latter is given by where , , . The case is discussed with the aid of a high-temperature expansion and of analysis of small systems. Specific heats and susceptibilities in special cases: (i) , , (ii) , , () , , () , , () , () are compared and it is shown that (i), (), and () have the characteristic features of the observed parallel susceptibility of an antiferromagnetic substance, (ii) those of perpendicular susceptibility, and () and () those of paramagnetic susceptibility, even though they have no singularities. The distribution of the zeros of the partition function is also discussed.
- Received 23 February 1962
DOI:https://doi.org/10.1103/PhysRev.127.1508
©1962 American Physical Society