positive, it implies an increase of this energy with increasing $M$, and hence a suppression of the $M(h)$ curve at fixed external field $h$. This is calculated in Ref., and reproduced in Appendix \[sec table\]. The result agrees very well with experimental data on [[Cs$_2$CuCl$_4$]{}]{}.

Consulting Table \[tab:dims\], one sees that of the remaining terms, the third and fourth terms are presumably most important. The third term involves $\mathcal{S}^z_{\pi\pm 2\delta}$ operators, whose scaling dimensions approach the minimal value of $1/2$ at small magnetization. Because this term lacks any derivatives, it achieves nearly the smallest total scaling dimension ($\approx 2 \times 1/2 =
1$) for small $M$. The fourth term contains a derivative (which adds $1$ to its scaling dimension), but contains $\mathcal{S}^\pm_\pi$ operators, whose scaling dimensions decrease from $1/2$ towards $1/4$ near saturation. Thus the total scaling dimension of the fourth term decreases from $2\times 1/2 + 1=2$ at small $M$ towards $2\times
1/4+1=1.5$ near saturation. This makes it less relevant than the third term at small $M$, but more relevant than it near saturation. The remaining (second and fifth) terms have larger scaling dimensions for all values of the magnetization.

We therefore drop these less relevant terms, as well 