i.e., $S_{\sigma}$. As discussed before, $S_{\sigma}$ describes two plausible phases, the weak coupling phase, in which the ground state is antiferromagnetically ordered, and the strong coupling phase, in which the ground state is gapped. The weak coupling phase is favored for large spin magnitudes $S$. Various numerical and analytical studies have consistently demonstrated that the ground state is always Néel ordered for simple quantum antiferromagnets on a $2d$ square lattice, even for the smallest possible spin value of $S=1/2$ [@Manousakis91]. For this reason, physicists have turned to frustrated spin models to look for exotic spin liquid states.

The NL$\sigma$M approach has generated interesting results when applied to weakly frustrated spin models, where the main effect of frustration is to reduce the effective coupling strength between rotors (for example, $J_1-J_2$ models, in which a next-nearest neighbor antiferromagnetic coupling is added to the Heisenberg model on a square lattice). In this case, it has been shown that spin-Peierls order can be obtained when discontinuous monopole-like spin configurations are included in the calculation of $S_T$ [@ReadSachdev90]. However, the method becomes questionable when applied to strongly frustrated spin systems, in which effective rotors become difficult to define locally, for example, the antiferromagnetic Heisenberg model 