Duality, Solitons, and Dilute-Gas Approximation in the One-DimensionalX−YModel with Symmetry-Breaking Fields

The continuous-transfer-matrix technique, together with the dilute-gas approximation, is used to study the thermodynamics and static properties of the linear-chain planar model. Explicit analytic expressions for the free-energy and spin-spin correlation functions, as a function of temperature, symmetry-breaking fields, and density of solitons, are given. The correlation length is predicted to increase exponentially as the temperature goes to zero. This result should be seen in elastic neutron scattering experiments on CsNi${\mathrm{F}}_3$.