Magnetization measurements have been performed on the amorphous alloys RE40Y23Cu37 (RE=Tb, Dy, Ho and Er) over a wide range of magnetic fields (0 to 7 Tesla) and temperatures. These systems show no spontaneous magnetization and are characterized as disordered magnets with random magnetic anisotropy (RMA). Although the low field susceptibility does not diverge it is close to the demagnetizing limit for T<or=TSG. The ratio D/J of the strength of the RMA axial crystal field parameter D to the ferromagnetic exchange parameter J, is large for these systems. The authors have performed a ferromagnetic-like scaling analysis of the magnetization data for large applied fields, thereby determining the critical RMA exponents, beta a, gamma a and delta a The non-linear susceptibility, chi nl, is taken to be the order parameter, as for canonical spin glasses; chi nl also shows critical behaviour. Both of these results point to a phase transition at TSG. The thermal variation of the high-field magnetization and also of the magnetostriction support this conclusion, as does the existence of transition lines of the de Almeida-Thouless type.