  We formulate the problem of finding the low-energy limit of spin foam models
as a coarse-graining problem in the sense of statistical physics. This suggests
that renormalization group methods may be used to find that limit. However,
since spin foams are models of spacetime at Planck scale, novel issues arise:
these microscopic models are sums over irregular, background-independent
lattices. We show that all of these issues can be addressed by the recent
application of the Kreimer Hopf algebra for quantum field theory
renormalization to non-perturbative statistical physics. The main difference
from standard renormalization group is that the Hopf algebra executes block
transformations in parts of the lattice only but in a controlled manner so that
the end result is a fully block-transformed lattice.
