2.3 Numerical implementation
Caracciolo and Pelissetto [63, 64, 65, 66, 67] performed a numerical investigation of the phase
structure of Smolin’s model. Using the compact group 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 44 and 84-lattices with periodic boundary
conditions) indicated strongly that the transition was first-order, even if the measure was generalized by a
factor of , .