Thermodynamics and correlations of the easy-plane ferromagnet CsNiF3

The ferromagnetic compound CsNiF3 has been the object of plenty of experimental and theoretical research, due to its apparent ID behavior (above the 3D ordering temperature TN=2.7 K). Indeed it can be modeled as a ferromagnetic chain with single-site easy-plane anisotropy. Its quantum Hamiltonian can also be expressed in terms of canonically conjugate operators by means of the Villain transformation, allowing us to apply a recently devised method, called the pure-quantum self-consistent harmonic approximation (PQSCHA), in order to obtain a classical effective Hamiltonian, by means of which the quantum thermal averages can be approximated by phase-space integrals. Comparing with the available quantum techniques, it is apparent that this is an enormous simplification. These classical-like formulas are able to describe the quantum behavior of the system, provided that the quantum coupling is not too strong. This is indeed the case for CsNiF3, whose effective Hamiltonian bears the form of the classical counterpart of the original one, but with suitably renormalized values of applied field, anisotropy, and exchange constant. An interesting feature is the appearance of an exchange anisotropy in competition with the easy-plane one, reflecting the effect of the quantum out-of-plane fluctuations. The classical transfer-matrix method is finally used in calculating various thermodynamic quantities, static structure factors and correlation lengths. Comparison with the available experimental data for CsNiF3, as well as with existing numerical simulation results, generally shows very good quantitative agreement.