Spin-correlation functions in sine-Gordon magnetic chains

For the one-dimensional easy plane ferromagnet in a symmetry breaking field and for the xy antiferromagnet with various in-plane anisotropies, the transfer operator method is used to calculate the static two-spin correlation functions at low temperatures, in the classical limit. Although both systems can be described approximately by the sine-Gordon equation, the solitons (which are solutions of this equation for the excitations) can have very different effects on physical quantities in the two systems. In the antiferromagnet, the order-parameter correlation length diverges with the distance between solitons in the low soliton density limit (as T0). The corresponding susceptibility diverges as well. However, for the ferromagnet, the corresponding soliton effects go to zero exponentially as T0. The physics behind this is discussed, and successful comparison is made with recent neutron inelastic scattering experiments on the ferromagnet CsNiF3 and on the antiferromagnet (CH3)N4MnCl3.