Coarse graining in spin foam models

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 the 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 the 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.