Phase Structure of Dynamical Triangulation Models in Three Dimensions

We discuss the geometry of dynamical triangulations associated with 3-dimensional and 4-dimensional simplicial quantum gravity. We provide analytical expressions for the canonical partition function in both cases, and study its large volume behavior. In the space of the coupling constants of the theory, we characterize the infinite volume line and the associated critical points. The results of this analysis are found to be in excellent agreement with the MonteCarlo simulation...

We confirm recent claims that, contrary to what was generally believed, the phase transition of the dynamical triangulation model of four-dimensional quantum gravity is of first order. We have looked at this at a volume of 64,000 four-simplices, where the evidence in the form of a double peak histogram of the action is quite clear.

We investigate a new phase structure of the three-dimensional dynamical triangulation model with an additional local term by Monte Carlo simulation. We find that the first order phase transition observed for the naive Einstein-Hilbert action terminates at a finite coefficient of the new term. The phase transition turns into second order at the endpoint, beyond which it becomes a crossover.

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.

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 study numerically the dynamical triangulation formulation of two-dimensional quantum gravity using a restricted class of triangulation, so-called minimal triangulations, in which only vertices of coordination number 5, 6, and 7 are allowed. A real-space RG analysis shows that for pure gravity (central charge c = 0) this restriction does not affect the critical behavior of the model. Furthermore, we show that the critical behavior of an Ising model coupled to minimal dynami...

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

In the weak-coupling limit, kappa_0 going to infinity, the partition function of simplicial quantum gravity is dominated by an ensemble of triangulations with the ratio N_0/N_D close to the upper kinematic limit. For a combinatorial triangulation of the D--sphere this limit is 1/D. Defining an ensemble of maximal triangulations, i.e. triangulations that have the maximal possible number of vertices for a given volume, we investigate the properties of this ensemble in three dim...

We conduct numerical simulations of a model of four dimensional quantum gravity in which the path integral over continuum Euclidean metrics is approximated by a sum over combinatorial triangulations. At fixed volume the model contains a discrete Einstein-Hilbert term with coupling $\kappa$ and local measure term with coupling $\beta$ that weights triangulations according to the number of simplices sharing each vertex. We map out the phase diagram in this two dimensional param...

We investigate a nonperturbative formulation of quantum gravity defined via Euclidean dynamical triangulations (EDT) with a non-trivial measure term in the path integral. We are motivated to revisit this older formulation of dynamical triangulations by hints from renormalization group approaches that gravity may be asymptotically safe and by the emergence of a semiclassical phase in causal dynamical triangulations (CDT). We study the phase diagram of this model and identify t...