Finite-temperature excitations and thermodynamics of theΔ>~1Heisenberg-Ising ring

We prove the existence and discuss the uniqueness of the solution of the equations proposed by Gaudin for the free energy of the $\Delta \ge 1$ Heisenberg-Ising ring. A numerical technique for solving the equations is outlined, and some results of the numerical work are displayed. Comparisons are made with the previous numerical study of Bonner and Fisher with favorable results, giving support to Gaudin's formulation. The finite-temperature excitations of the system are derived, and some sample dispersion curves are given.