Quantum effects in quasi-one-dimensional magnetic systems

Quantum statistics for the field theory in 1 + 1 dimensions developed by Takayama and the author is applied to the quasi-one-dimensional magnetic system like CsNi${\mathrm{F}}_3$ and ${\left(\mathrm{C}{\mathrm{H}}_3\right)}_4$NMn${\mathrm{Cl}}_3$ (TMMC) in magnetic fields. For $T\gg m$ where $T$ is the temperature and $m$ is the magnon mass of the system the most significant quantum effects are the mass renormalization; the magnon mass and the soliton mass are reduced from the classical values. This appears to account for the discrepancies between the classical soliton mass and the observed soliton mass in CsNi${\mathrm{F}}_3$ and TMMC.