Amorphous Gd7-xDyxNi3 is a model random anisotropy system in which the
exchange J can be varied whilst maintaining a constant single ion ani
sotropy D. Investigation of the magnetic phase diagram as x, and hence
D/J, increases reveals a re-entrant transition from correlated sperom
agnet to speromagnet for x < 4, while for x > 4 the paramagnetic-spero
magnetic transition is direct. A multicritical point is observed at x
= 4, at which the exponent gamma increases suddenly from 1.35 to 2.