Causal Dynamical Triangulations (CDT) are a concrete attempt to define a nonperturbative path integral for quantum gravity. We present strong evidence that the lattice theory has a second-order phase transition line, which can potentially be used to define a continuum limit in the conventional sense of nongravitational lattice theories.
@article{arxiv.1108.3932,
title = {A second-order phase transition in CDT},
author = {J. Ambjorn and S. Jordan and J. Jurkiewicz and R. Loll},
journal= {arXiv preprint arXiv:1108.3932},
year = {2011}
}