The phase diagram and mean local field theory for ensembles of dipolar inte
racting ellipsoidal nanoparticles randomly distributed over the sites of a
tetragonal lattice are constructed. Dipolar ferromagnetism in the ensembles
arises from a competition between the ferro- and antiferromagnetic interac
tions of the nanoparticle magnetic moments. A critical temperature is defin
ed for these systems with magnitude depending on the shape of the nanoparti
cles.