  We prove the uniqueness of homogeneous blow-up limits of maps minimizing the
modified Ericksen energy for nematic liquid crystals in a planar domain. The
proof is based on the Weiss monotonicity formula, and a blow-up argument,
originally due to Allard and Almgren \cite{AA} for minimal surfaces, and L.
Simon \cite{SL} for energy-minimizing maps into analytic targets, which
exploits the integrability of certain Jacobi fields.
