The three-dimensional diluted antiferromagnet in a magnetic field has a lon
ge-range ordered state for sufficiently low temperatures and external field
s. We study the irreversibilities at the phase transition from this state i
nto the paramagnetic state at higher temperatures. Performing field cooling
and zero field cooling simulation procedures we find a small irreversibili
ty in the internal energy and the specific heat, although the behavior of t
he order parameter is irreversible and the phase transition is suppressed i
n the FC case. The specific heat shows a noncritical broad maximum above th
e transition temperature T-c. The results are compatible with recent experi
mental results obtained by Satooka et al., whereas our interpretation of th
e data is different.