Let $\Omega \subset{\bf R}^3$ be a smooth bounded domain and consider the energy functional ${\mathcal J}_{\varepsilon} (m; \Omega) := \int_{\Omega} \left ( \frac{1}{2 \varepsilon} |Dm|^2 + \psi(m) + \frac{1}{2} |h-m|^2 \right) dx + \frac{1}{2} \int_{{\bf R}^3} |h_m|^2 dx. $ Here $\varepsilon>0$ is a small parameter and the admissible function m lies in the Sobolev space of vector-valued functions $W^{1,2}(\Omega;{\bf R}^3)$ and satisfies the pointwise constraint $|m(x)|=1$ for a.e. $x \...