Abstract
The exact solution is given for a linear chain of atoms of spin ½ coupled together by the anisotropic Hamiltonian The energy of the antiferromagnetic ground state is computed and comparison is made with a variational method. The parameter is allowed to vary between 0 and 1, regulating the relative amount of Ising anisotropy. The short-range order, , is calculated exactly from the variation of the ground-state energy with . It is shown that a kink in the short-range order curve calculated using the variational method is fictitious, and the associated discontinuity in is nonexistent. A discussion is given of long-range order and criticisms are presented regarding the predictions of the variational method.
- Received 16 June 1958
DOI:https://doi.org/10.1103/PhysRev.112.309
©1958 American Physical Society