  We study, by means of magnetic susceptibility and magnetic aging experiments,
the nature of the glassy magnetic dynamics in arrays of Co nanoparticles,
self-organized in N layers from N=1 (two-dimensional limit) up to N=20
(three-dimensional limit). We find no qualitative differences between the
magnetic responses measured in these two limits, in spite of the fact that no
spin-glass phase is expected above T=0 in two dimensions. More specifically,
all the phenomena (critical slowing down, flattening of the field-cooled
magnetization below the blocking temperature and the magnetic memory induced by
aging) that are usually associated with this phase look qualitatively the same
for two-dimensional and three-dimensional arrays. The activated scaling law
that is typical of systems undergoing a phase transition at zero temperature
accounts well for the critical slowing down of the dc and ac susceptibilities
of all samples. Our data show also that dynamical magnetic correlations
achieved by aging a nanoparticle array below its superparamagnetic blocking
temperature extend mainly to nearest neighbors. Our experiments suggest that
the glassy magnetic dynamics of these nanoparticle arrays is associated with a
zero-temperature spin-glass transition.
