Linear Antiferromagnetic Chain with Anisotropic Coupling

The exact solution is given for a linear chain of N atoms of spin coupled together by the anisotropic Hamiltonian H=2Ji=1{S₈}^z{S₈+₁}^z+ (1-) ({S₈}^x{S₈+₁}^x+{S₈}^y{S₈+₁}^y). 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, i^{S₈}^z{S₈+₁}^z, 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 {^2E}{^2} is nonexistent. A discussion is given of long-range order and criticisms are presented regarding the predictions of the variational method.