arXiv subjects
Publications and source records attributed to R. Renken.
We show that the phase transition previously observed in dynamical triangulation models of quantum gravity can be understood as being due to the creation of a singular link. The transition between singular and non-singular geometries as the gravitational coupling is varied appears to be first order.
We consider two issues in the DT model of quantum gravity. First, it is shown that the triangulation space for D>3 is dominated by triangulations containing a single singular (D-3)-simplex composed of vertices with divergent dual volumes. Second we study the ergodicity of current simulation algorithms. Results from runs conducted close to the phase transition of the four-dimensional theory are shown. We see no strong indications of ergodicity br eaking in the simulation and our data support recent claims that the transition is most probably first order. Furthermore, we show that the critical properties of the system are determined by the dynamics of remnant singular vertices.
By a sequence of numerical experiments we demonstrate that generic triangulations of the $D-$sphere for $D>3$ contain one {\it singular} $(D-3)-$simplex. The mean number of elementary $D-$simplices sharing this simplex increases with the volume of the triangulation according to a simple power law. The lower dimension subsimplices associated with this $(D-3)-$simplex also show a singular behaviour. Possible consequences for the DT model of four-dimensional quantum gravity are discussed.
We measure numerically the distribution of baby universes in the crumpled phase of the dynamical triangulation model of 4d quantum gravity. The relevance of the results to the issue of an exponential bound is discussed. The data are consistent with the existence of such a bound.
We present numerical results supporting the existence of an exponential bound in the dynamical triangulation model of three-dimensional quantum gravity.Both the critical coupling and various other quantities show a slow power law approach to the infinite volume limit.
We have studied a model which has been proposed as a regularisation for four dimensional quantum gravity. The partition function is constructed by performing a weighted sum over all triangulations of the four sphere. Using numerical simulation we find that the number of such triangulations containing $V$ simplices grows faster than exponentially with $V$. This property ensures that the model has no thermodynamic limit.
We present the results of a high statistics Monte Carlo study of a model for four dimensional euclidean quantum gravity based on summing over triangulations. We show evidence for two phases; in one there is a logarithmic scaling on the mean linear extent with volume, whilst the other exhibits power law behaviour with exponent 1/2. We are able to extract a finite size scaling exponent governing the growth of the susceptibility peak
We study the XY model on a lattice with fluctuating connectivity. The expectation is that at an appropriate critical point such a system corresponds to a compactified boson coupled to 2d quantum gravity. Our simulations focus, in particular, on the important topological features of the system. The results lend strong support to the two phase structure predicted on the basis of analytical calculations. A careful finite size scaling analysis yields estimates for the critical exponents in the low temperature phase.