  Understanding the large-scale physics is crucial for the spin foam approach
to quantum gravity. We tackle this challenge from a statistical physics
perspective using simplified, yet feature-rich models. In particular, this
allows us to explicitly answer whether broken symmetries will be restored by
renormalization: We observe a weak phase transition in both Migdal-Kadanoff and
tensor network renormalization. In this work we give a concise presentation of
the concepts, results and promises of this new direction of research.
