301 research outputs found
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
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
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
Entropy and the Approach to the Thermodynamic Limit in Three-Dimensional Simplicial Gravity
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
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
Spectroscopy, Equation Of State And Monopole Percolation In Lattice QED With Two Flavors
Non-compact lattice QED with two flavors of light dynamical quarks is
simulated on lattices, and the chiral condensate, monopole density and
susceptibility and the meson masses are measured. Data from relatively high
statistics runs at relatively small bare fermion masses of 0.005, 0.01, 0.02
and 0.03 (lattice units) are presented. Three independent methods of data
analysis indicate that the critical point occurs at and that
the monopole condensation and chiral symmetry breaking transitions are
coincident. The monopole condensation data satisfies finite size scaling
hypotheses with critical indices compatible with four dimensional percolation.
The best chiral equation of state fit produces critical exponents
(, ) which deviate significantly from mean
field expectations. Data for the ratio of the sigma to pion masses produces an
estimate of the critical index in good agreement with chiral
condensate measurements. In the strong coupling phase the ratio of the meson
masses are ,
and , while on the weak coupling side of the
transition , ,
indicating the restoration of chiral symmetry.\footnote{\,^{}}{August 1992}Comment: 21 pages, 24 figures (not included
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
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
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\u3e3 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
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