ISING-LINK REGGE GRAVITY

We define a simplified version of Regge quantum gravity where the link lengths can take on only two possible values, both always compatible with the triangle inequalities. This is therefore equivalent to a model of Ising spins living on the links of a regular lattice with somewhat complicated, yet local interactions. The measure corresponds to the natural sum over all 2 links configurations, and numerical simulations can be efficiently implemented by means of look-up tables. In three dimensions we find a peak in the curvature susceptibility which grows with increasing system size. The value of the corresponding critical exponent appears to vary with the cosmological constant, agreeing with Regge gravity for at least one value of. However, the curvature does not go to zero at the transition. © 1994 The American Physical Society.