Recently, I and Fotini Markopoulou rewrote the Causal Dynamical Triangulations model as a spin system and provided a new method of solution of the model. The model was studies before this by Ambjorn (Niels Bohr Institute), Anagnostopoulos (Univ. of Crete) and Loll(Institute for Theoretical Physics, Utrecht University). They invented this path integral approach toward 2d quantum gravity and applied the generating functional method in their solution. (Refrence)
In addition, they have extended the model to higher dimensions (refrence) and coupled it to matter (refrence). It is interesting that a 4 dimensional spacetime is emereged by gluing 4 simplices in a specific way.
Now one can have enough fun with the new approach to the solution of the 2 dimensional model, RG transform its couplings easliy and predict the value of cosmological constant!
These models are based on the notion of the existence of a pre-assumed time in the universe and construction is led into that direction, otherwise the dimensionality of the global spacetime grows fast to infinity.
(The paper - more pictures)