The Heisenberg spin glass is considered in the presence of two anisotropy f
ields, namely, the uniaxial and cubic ones. The Gabay-Toulouse line, which
signals the onset of transverse spin-glass ordering with respect to an exte
rnal magnetic field, exhibits novel behavior due to the presence of the ani
sotropy fields; in particular, reentrance effects may occur. Possible relat
ions with experimental observations are discussed. (C) 2001 Elsevier Scienc
e B.V. All rights reserved.