I think it is unlikely that a lattice gravity model will correctly describe the quantum theory of gravitation any time soon,
although the odds have improved somewhat with new results about asymptotic safety.
While such models have interesting properties, as far as I know a reasonable continuum limit has never been demonstrated.
A few days ago Simon Catterall et al. published results for a model which goes back to the simulations of
Menotti & Pelissetto, but with an additional Wilson term in the action and thus an additional coupling
parameter. They find an interesting transition for a certain threshold value of this parameter and conclude that
"It remains to be seen whether this threshold value can be thought of as a true critical value and if so
whether this critical value corresponds to a continuous or discontinuous phase transition. The latter issue is
of course a crucial issue to address in the context of obtaining a non-trivial continuum limit."
Perhaps I should dust off our lattice gravity code(s) and see what they can do on new and better hardware.
It would be a nice (but almost certainly completely useless) project for 2010...
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