  Tensor models are a generalization of matrix models (their graphs being dual
to higher-dimensional triangulations) and, in their colored version, admit a
1/N expansion and a continuum limit. We introduce a new class of colored tensor
models with a modified propagator which allows us to associate weight factors
to the faces of the graphs, i.e. to the bones (or hinges) of the triangulation,
where curvature is concentrated. They correspond to dynamical triangulations in
three and higher dimensions with generalized amplitudes. We solve analytically
the leading order in 1/N of the most general model in arbitrary dimensions. We
then show that a particular model, corresponding to dynamical triangulations
with a non-trivial measure factor, undergoes a third-order phase transition in
the continuum characterized by a jump in the susceptibility exponent.
