118 research outputs found
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
. 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
Scaling Exponents in Quantum Gravity near Two Dimensions
We formulate quantum gravity in 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 limit. The theory possesses the ultraviolet
fixed point as long as the central charge , 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 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
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
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
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
Towards a Non-Perturbative Renormalization of Euclidean Quantum Gravity
A real space renormalization group technique, based on the hierarchical
baby-universe structure of a typical dynamically triangulated manifold, is used
to study scaling properties of 2d and 4d lattice quantum gravity. In 4d, the
-function is defined and calculated numerically. An evidence for the
existence of an ultraviolet stable fixed point of the theory is presentedComment: 12 pages Latex + 1 PS fi
Ising Model Coupled to Three-Dimensional Quantum Gravity
We have performed Monte Carlo simulations of the Ising model coupled to
three-dimensional quantum gravity based on a summation over dynamical
triangulations. These were done both in the microcanonical ensemble, with the
number of points in the triangulation and the number of Ising spins fixed, and
in the grand canoncal ensemble. We have investigated the two possible cases of
the spins living on the vertices of the triangulation (``diect'' case) and the
spins living in the middle of the tetrahedra (``dual'' case). We observed phase
transitions which are probably second order, and found that the dual
implementation more effectively couples the spins to the quantum gravity.Comment: 11 page
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 , which is known to be unrecognizable, but see no sign of these
unreachable states.Comment: 8 pages, LaTeX2e source with postscript resul
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