Caracciolo and Pelissetto [63,
64,
65,
66,
67] performed a numerical investigation of the phase structure of
Smolin's model. Using the compact group
SO
(5) and its associated Haar measure, their findings confirmed the
two-phase structure: a strong-coupling phase with a confining
property and presence of exponential clustering, and a
weak-coupling phase dominated by a class of topological
configurations, with vanishing vierbein. However, their Monte
Carlo data (on
and
-lattices with periodic boundary conditions) indicated strongly
that the transition was first-order, even if the measure was
generalized by a factor of
,
[67].