  We analyze generalizations of the Schwinger model with more massless fermions
and more vector fields. We focus on models with the gauge structure of
``diagonal color $SU(n)$'' but unlike previous investigators, we do not assume
that all the gauge boson masses are the same. Unlike the Schwinger model, these
are Banks-Zaks models with conformal sectors that survive at long distances. In
addition to local operators that go to ``unparticle operators'' with non-zero
anomalous dimensions at long distances, they contain local operators like the
$\bar\psi_L\psi_R$ operator in the Schwinger model which go to constants at
long distances. These operators have calculable vacuum expectation values (up
to phases). Cluster decomposition applied to correlation functions involving
these operators yields nontrivial and calculable non-perturbative constraints
on correlation functions. One consequence is ``conformal coalescence'' in which
linear combinations of short distance operators disappear from the
long-distance theory, leaving only one kind of unparticle stuff in the
low-energy theory. We believe that our detailed analysis of diagonal color
$SU(n)$ paints an appealing picture of unparticle operators as the result of an
incomplete binding of the massless fermions. We complete the picture (and the
binding) by analyzing the diagonal color $U(n)$ model with a very small $U(1)$
coupling and thus a gauge boson with a dynamical mass much smaller than the
other masses in the model. This model has a mass gap and we can see explicitly
the transition from free-fermion behavior at short distances to unparticle
physics at intermediate distances to the physics of massive particles at long
distances.
