Critical Behavior of Dynamically Triangulated Quantum Gravity in Four Dimensions

We performed detailed study of the phase transition region in Four Dimensional Simplicial Quantum Gravity, using the dynamical triangulation approach. The phase transition between the Gravity and Antigravity phases turned out to be asymmetrical, so that we observed the scaling laws only when the Newton constant approached the critical value from perturbative side. The curvature susceptibility diverges with the scaling index $-.6$. The physical (i.e. measured with heavy particle propagation) Hausdorff dimension of the manifolds, which is 2.3 in the Gravity phase and 4.6 in the Antigravity phase, turned out to be 4 at the critical point, within the measurement accuracy. These facts indicate the existence of the continuum limit in Four Dimensional Euclidean Quantum Gravity.Comment: 12pg

Scaling and the Fractal Geometry of Two-Dimensional Quantum Gravity

We examine the scaling of geodesic correlation functions in two-dimensional gravity and in spin systems coupled to gravity. The numerical data support the scaling hypothesis and indicate that the quantum geometry develops a non-perturbative length scale. The existence of this length scale allows us to extract a Hausdorff dimension. In the case of pure gravity we find d_H approx. 3.8, in support of recent theoretical calculations that d_H = 4. We also discuss the back-reaction of matter on the geometry.Comment: 16 pages, LaTeX format, 8 eps figure

More on the exponential bound of four dimensional simplicial quantum gravity

A crucial requirement for the standard interpretation of Monte Carlo simulations of simplicial quantum gravity is the existence of an exponential bound that makes the partition function well-defined. We present numerical data favoring the existence of an exponential bound, and we argue that the more limited data sets on which recently opposing claims were based are also consistent with the existence of an exponential bound.Comment: 10 pages, latex, 2 figure

Singular Vertices in the Strong Coupling Phase of Four--Dimensional Simplicial Gravity

We study four--dimensional simplicial gravity through numerical simulation with special attention to the existence of singular vertices, in the strong coupling phase, that are shared by abnormally large numbers of four--simplices. The second order phase transition from the strong coupling phase into the weak coupling phase could be understood as the disappearance of the singular vertices. We also change the topology of the universe from the sphere to the torus.Comment: 10 pages, six PostScript figures; figures are also available at http://hep-th.phys.s.u-tokyo.ac.jp/~izubuchi/paper/4dqg

Scaling Exponents in Quantum Gravity near Two Dimensions

We formulate quantum gravity in $2+\epsilon$ dimensions in such a way that the conformal mode is explicitly separated. The dynamics of the conformal mode is understood in terms of the oversubtraction due to the one loop counter term. The renormalization of the gravitational dressed operators is studied and their anomalous dimensions are computed. The exact scaling exponents of the 2 dimensional quantum gravity are reproduced in the strong coupling regime when we take $\epsilon\rightarrow0$ limit. The theory possesses the ultraviolet fixed point as long as the central charge $c<25$, which separates weak and strong coupling phases. The weak coupling phase may represent the same universality class with our Universe in the sense that it contains massless gravitons if we extrapolate $\epsilon$ up to 2.Comment: 24 pages and 1 figure, UT-614, TIT/HEP-191 and YITP/U-92-05 (figures added to the 1st version

Absence of barriers in dynamical triangulation

Due to the unrecognizability of certain manifolds there must exist pairs of triangulations of these manifolds that can only be reached from each other by going through an intermediate state that is very large. This might reduce the reliability of dynamical triangulation, because there will be states that will not be reached in practice. We investigate this problem numerically for the manifold $S^5$, which is known to be unrecognizable, but see no sign of these unreachable states.Comment: 8 pages, LaTeX2e source with postscript resul

Simplicial Gravity in Dimension Greater than Two

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.Comment: Talk presented at LATTICE96(gravity

Phase Structure of Four Dimensional Simplicial Quantum Gravity

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 peakComment: 11 pages (5 figures

Further evidence that the transition of 4D dynamical triangulation is 1st order

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.Comment: 12 pages, LaTeX2

Scaling Structures in Four-dimensional Simplicial Gravity

Four-dimensional(4D) spacetime structures are investigated using the concept of the geodesic distance in the simplicial quantum gravity. On the analogy of the loop length distribution in 2D case, the scaling relations of the boundary volume distribution in 4D are discussed in various coupling regions i.e. strong-coupling phase, critical point and weak-coupling phase. In each phase the different scaling relations are found.Comment: 4 pages, latex, 4 ps figures, uses espcrc2.sty. Talk presented at LATTICE96(gravity). All figures and its captions have been improve