  Random tensor models which display multicritical behaviors in a remarkably
simple fashion are presented. They come with entropy exponents \gamma =
(m-1)/m, similarly to multicritical random branched polymers. Moreover, they
are interpreted as models of hard dimers on a set of random lattices for the
sphere in dimension three and higher. Dimers with their exclusion rules are
generated by the different interactions between tensors, whose coupling
constants are dimer activities. As an illustration, we describe one
multicritical point, which is interpreted as a transition between the dilute
phase and a crystallized phase, though with negative activities.
