  We study perturbation theory for spin foam models on triangulated manifolds.
Starting with any model of this sort, we consider an arbitrary perturbation of
the vertex amplitudes, and write the evolution operators of the perturbed model
as convergent power series in the coupling constant governing the perturbation.
The terms in the power series can be efficiently computed when the unperturbed
model is a topological quantum field theory. Moreover, in this case we can
explicitly sum the whole power series in the limit where the number of
top-dimensional simplices goes to infinity while the coupling constant is
suitably renormalized. This `dilute gas limit' gives spin foam models that are
triangulation-independent but not topological quantum field theories. However,
we show that models of this sort are rather trivial except in dimension 2.
