Failure of the classical approximation for CsNiF3

An exact numerical-transfer-matrix method is used to calculate the thermodynamic properties of an easy-plane Heisenberg ferromagnet with in-plane magnetic field. The results clearly show that the often-adopted classical approximation is totally inadequate for CsNi${\mathrm{F}}_3$ in typical experimental circumstances. In particular, it is shown that a quantum treatment of the out-of-plane fluctuations is crucial.