Soliton specific heat of spin chains: Limitations of the quantum sine-Gordon model

We compare the exact quantum sine-Gordon (SG) specific-heat calculation of Fowler and Zotos [Phys. Rev. B 24, 2634 (1981); 25, 2806 (1982)] with measurements of ${\mathrm{CsNiF}}_3$, TMMC [(${\mathrm{CH}}_3$ ${)}_4$ ${\mathrm{NMnCl}}_3$], and CHAB [(${\mathrm{C}}_6$ ${\mathrm{H}}_{11}$ ${\mathrm{NH}}_3$)${\mathrm{CuBr}}_3$]. These compounds have all been described qualitatively as classical SG systems. Quantum corrections slightly improve the quantitative agreement with experiment for ${\mathrm{CsNiF}}_3$, but result in worse agreement for TMMC and CHAB. Hence the SG model is not an adequate representation of the spin chain particularly in the latter two cases, presumably because of its neglect of out-of-plane fluctuations. Especially in the case of TMMC, an acceptable theory will need to include in the statistical mechanics an accurate quantum treatment of out-of-plane motion.