arXiv subjects
Publications and source records attributed to Ray Renken.
We use Monte Carlo simulation to study the phase diagram of three-dimensional dynamical triangulations with a boundary. Three phases are indentified and characterized. One of these phases is a new, boundary dominated phase; a simple argument is presented to explain its existence. First-order transitions are shown to occur along the critical lines separating phases.
A block spin renormalization group approach is proposed for the dynamical triangulation formulation of two-dimensional quantum gravity. The idea is to update link flips on the block lattice in response to link flips on the original lattice. Just as the connectivity of the original lattice is meant to be a lattice representation of the metric, the block links are determined in such a way that the connectivity of the block lattice represents a block metric. As an illustration, this approach is applied to the Ising model coupled to two-dimensional quantum gravity. The correct critical coupling is reproduced, but the critical exponent is obscured by unusually large finite size effects.
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. However, the value of the corresponding critical exponent as well as the behavior of the curvature at the transition differ from that found by Hamber and Williams for the Regge theory with continuously varying link lengths.