  We study in this paper the Heisenberg antiferromagnet with nearest neighbours
interactions on the Husimi cactus, a system which has locally the same topology
as the Kagom\'e lattice. This system has a huge classical degeneracy
corresponding to an extensive number of degrees of freedom.We show that unlike
thermal fluctuations, quantum fluctuations lift partially this degeneracy and
favour a discrete subset of classical ground states. In order to clarify the
origin of these effects, we have set up a general semi-classical analysis of
the order from disorder phenomenon and clearly identified the differences
between classical and quantum fluctuations. This semi-classical approach also
enables us to classify various situations where a selection mechanism still
occurs. Moreover, once a discrete set of ground states has been preselected,
our analysis suggests that tunelling processes within this set should be the
dominant effect underlying the strange low energy spectrum of Kagom\'e-like
lattices.
