Realization of a Witten Critical Theory in(CH3)4NMnCl3

The exact $T=0\mathrm{}$ susceptibility times spin-wave velocity of an isotropic spin-$s$ antiferromagnetic chain is calculated by use of the Wess-Zumino-Witten $\sigma$ model, with Kac-Moody central charge $k=2s$, as the critical theory. The result, ${\chi \upsilon }_s=\frac{k}{2\pi }$, agrees exactly with Bethe-Ansatz results for integrable models and well with numerical results ($s=\frac{1}{2}$), Fisher's classical limit, and experiments on Cu${\mathrm{Cl}}_2$ · 2N${\mathrm{C}}_5$ ${\mathrm{H}}_5$ ($s=\frac{1}{2}$) and ${\left(\mathrm{C}{\mathrm{H}}_3\right)}_4$NMn${\mathrm{Cl}}_3$ ($s=\frac{5}{2}$). (${\chi }_{\parallel }$ is also calculated exactly for $s=\frac{1}{2}$ and arbitrary planar anisotropy.) This suggests that ${\left(\mathrm{C}{\mathrm{H}}_3\right)}_4$NMn${\mathrm{Cl}}_3$ is an experimental realization of this new universality class.