Quantum statistics of easy-plane ferromagnetic chains and specific heat of ${\mathrm{CsNiF}}_3$ and (${\mathrm{C}}_6$${\mathrm{H}}_{11}$${\mathrm{NH}}_3$)${\mathrm{CuBr}}_3$

The field-dependent specific heat of two easy-plane ferromagnetic chains is calculated with extrapolation of numerical results for finite chains. Quantum statistics is applied for the corresponding spin-1 and spin-(1/2) Hamiltonians with single-site and exchange anisotropy, respectively. A drastic reduction of the excess in the specific heat, with respect to that found for the classical and sine-Gordon models, is obtained. The results are compared with the experimental data for ${\mathrm{CsNiF}}_3$ and (${\mathrm{C}}_6$ ${\mathrm{H}}_{11}$ ${\mathrm{NH}}_3$)${\mathrm{CuBr}}_3$. A semiquantitative agreement only is found as the heights of the maxima in the excess specific heat agree rather well with experiment but the peak positions are still not reproduced accurately.