Quantum thermodynamics of easy-plane ferromagnetic chains

We study the thermodynamics of ferromagnetic chains with single-ion easy-plane anisotropy and applied field. The Villain transformation puts its Hamiltonian in the starting form for the usual approximations in terms of sine-Gordon-like models, which may contain "mixed" terms in the canonical variables. Using a variational approach, we approximate the quantum partition function by a classical-like phase space integral with an effective Hamiltonian. The latter is similar to the original one, with quantum renormalized parameters. Our calculations of the specific heat strongly correct the classical model and are in very good agreement with the experimental data for CsNiF3.