The random-field Ising model (RFIM) system Fe0.42Zn0.58F2 is Studied by mag
netization and dynamic susceptibility measurements, under finite de applied
fields (H). For H < 20 kOe, the magnetic behaviour is compatible with a lo
ng-range ordered (LRO) antiferromagnetic (AF) ground state, which undergoes
a phase transition (PT) at a critical temperature T-c(H). For higher H, th
e LRO configuration becomes unstable and the PT is destroyed. A glassy dyna
mics emerges in the upper part of the (H, T) phase diagram. Our results rec
oncile earlier concepts associated with the weak RFIM problem with recent e
xperimental data in FexZn1-xF2.