Gabay-Toulouse Phase Transition in Heisenberg Spin-Glasses in Three Dimensions

We examine three-dimensional $\pm J$ Heisenberg models with and without random anisotropies in a magnetic field. We calculate both the stiffness exponent ${\theta }_s$ at absolute zero temperature and spin-glass correlation lengths for the longitudinal and transverse spin components at finite temperatures. We suggest that, contrary to a chirality scenario predicted by Kawamura and his co-workers, a Gabay-Toulouse phase transition occurs when the anisotropies are absent, although no phase transition occurs when they are present.