Steepest descent approach to the domain-wall thermodynamics of a classical easy-plane ferromagnetic chain: Application to CsNiF3

We derive asymptotic low-temperature expressions for the free energy, the specific heat, and the magnetization of the classical easy-plane Heisenberg chain in a field. At low field the system forms a stable gas of spin waves and domain walls. In a temperature-broadened region about a characteristic field given by the anisotropy, the domain-wall gas becomes unstable and dissociates into spin waves. At higher fields the domain-wall gas is absent. Applying our results to CsNi${\mathrm{F}}_3$ we find qualitative agreement.