Spin-correlation functions in sine-Gordon magnetic chains

For the one-dimensional easy plane ferromagnet in a symmetry breaking field and for the $\mathrm{xy}$ 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 $T\to 0$). The corresponding susceptibility diverges as well. However, for the ferromagnet, the corresponding soliton effects go to zero exponentially as $T\to 0$. The physics behind this is discussed, and successful comparison is made with recent neutron inelastic scattering experiments on the ferromagnet CsNi${\mathrm{F}}_3$ and on the antiferromagnet (C${\mathrm{H}}_3$)${}_4{}^{}{}_{}{}^{}\mathrm{N}$Mn${\mathrm{Cl}}_3$.