Transfer integral and collective coordinate results for the free energy of a classical 1D uniaxial Heisenberg ferromagnet

Two approaches to the evaluation of the partition function of the classical, one-dimensional Heisenberg ferromagnet with single-site anisotropy are examined: (i) a functional (transfer) integral method; and (ii) a steepest descent-collective coordinate scheme. It is found that the low-T static free energy expressions agree if all continuous symmetries (translation and rotation) are properly included. The contributions from non-linear domain wall excitations are explicit in approach (ii), and the present example extends previous similar investigations of single order-parameter component one-dimensional models.