23 research outputs found
A Renormalization Group for Dynamical Triangulations in Arbitrary Dimensions
A block spin renormalization group approach is proposed for the dynamical
triangulation formulation of quantum gravity in arbitrary dimensions.
Renormalization group flow diagrams are presented for the three-dimensional and
four-dimensional theories near their respective transitions.Comment: 18 pages, 6 postscript figures, revte
Non-Perturbative Renormalization Group Flows in Two-Dimensional Quantum Gravity
Recently a block spin renormalization group approach was proposed for the
dynamical triangulation formulation of two-dimensional quantum gravity. We use
this approach to examine non-perturbatively a particular class of higher
derivative actions for pure gravity.Comment: 17 page
Three-Dimensional Quantum Gravity Coupled to Gauge Fields
We show how to simulate U(1) gauge fields coupled to three-dimensional
quantum gravity and then examine the phase diagram of this system. Quenched
mean field theory suggests that a transition separates confined and deconfined
phases (for the gauge matter) in both the negative curvature phase and the
positive curvature phase of the quantum gravity, but numerical simulations find
no evidence for such transitions.Comment: 16 page
Phase Structure of Dynamical Triangulation Models in Three Dimensions
The dynamical triangulation model of three-dimensional quantum gravity is
shown to have a line of transitions in an expanded phase diagram which includes
a coupling mu to the order of the vertices. Monte Carlo renormalization group
and finite size scaling techniques are used to locate and characterize this
line. Our results indicate that for mu < mu1 ~ -1.0 the model is always in a
crumpled phase independent of the value of the curvature coupling. For mu < 0
the results are in agreement with an approximate mean field treatment. We find
evidence that this line corresponds to first order transitions extending to
positive mu. However, the behavior appears to change for mu > mu2 ~ 2-4. The
simplest scenario that is consistent with the data is the existence of a
critical end point
Numerical Study of c\u3e1 Matter Coupled to Quantum Gravity
We present the results of a numerical simulation aimed at understanding the nature of the `c = 1 barrier\u27 in two dimensional quantum gravity. We study multiple Ising models living on dynamical \phi^3 graphs and analyse the behaviour of moments of the graph loop distribution. We notice a universality at work as the average properties of typical graphs from the ensemble are determined only by the central charge. We further argue that the qualitative nature of these results can be understood from considering the effect of fluctuations about a mean field solution in the Ising sector
Nonperturbative Renormalization-Group Flows In 2-Dimensional Quantum-Gravity
Recently a block spin renormalization group approach was proposed for the dynamical triangulation formulation of two-dimensional quantum gravity. We use this approach to examine non-perturbatively a particular class of higher derivative actions for pure gravity
Scaling Behavior Of The Ising-Model Coupled To 2-Dimensional Quantum-Gravity
We study the Ising model on dynamical phi(3) graphs with spherical topology. A finite-size scaling analysis is carried out both with and without an external field leading to numerical estimates for various critical exponents which are in good agreement with analytical calculations. We further determine the equation of state, and measure the correlation of Ising spins on the ensemble of graphs
Three Dimensional Quantum Gravity Coupled to Ising Matter
We establish the phase diagram of three--dimensional quantum gravity coupled
to Ising matter. We find that in the negative curvature phase of the quantum
gravity there is no disordered phase for ferromagnetic Ising matter because the
coordination number of the sites diverges. In the positive curvature phase of
the quantum gravity there is evidence for two spin phases with a first order
transition between them.Comment: 12 page
Numerical Study of c>1 Matter Coupled to Quantum Gravity
We present the results of a numerical simulation aimed at understanding the
nature of the `c = 1 barrier' in two dimensional quantum gravity. We study
multiple Ising models living on dynamical graphs and analyse the
behaviour of moments of the graph loop distribution. We notice a universality
at work as the average properties of typical graphs from the ensemble are
determined only by the central charge. We further argue that the qualitative
nature of these results can be understood from considering the effect of
fluctuations about a mean field solution in the Ising sector.Comment: 12 page
The Block Spin Renormalization Group Approach and Two-Dimensional Quantum Gravity
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.Comment: 10 page