914 research outputs found
The Weak-Coupling Limit of 3D Simplicial Quantum Gravity
We investigate the weak-coupling limit, kappa going to infinity, of 3D
simplicial gravity using Monte Carlo simulations and a Strong Coupling
Expansion. With a suitable modification of the measure we observe a transition
from a branched polymer to a crinkled phase. However, the intrinsic geometry of
the latter appears similar to that of non-generic branched polymer, probable
excluding the existence of a sensible continuum limit in this phase.Comment: 3 pages 4 figs. LATTICE99(Gravity
Beyond the c=1 Barrier in Two-Dimensional Quantum Gravity
We introduce a simple model of touching random surfaces, by adding a chemical
potential rho for ``minimal necks'', and study this model numerically coupled
to a Gaussian model in d-dimensions (for central charge c = d = 0, 1 and 2).
For c <= 1, this model has a phase transition to branched polymers, for
sufficiently large rho. For c = 2, however, the extensive simulations indicate
that this transition is replaced by a cross-over behavior on finite lattices
--- the model is always in the branched polymer phase. This supports recent
speculations that, in 2d-gravity, the behavior observe in simulations for , is dominated by finite size effects, which are exponentially enhanced
as c -> 1+.Comment: 5 pages, 6 eps-figure
Scaling with a modified Wilson action which suppresses Z_2 artifacts in SU(2) lattice gauge theories
A modified Wilson action which suppresses plaquettes which take negative
values is used to study the scaling behavior of the string tension. The use of
the \b_E scheme gives good agreement with asymptotic two loop results.Comment: Latex (ps figure appended in the end), 7 page
The Ising Model on a Quenched Ensemble of c = -5 Gravity Graphs
We study with Monte Carlo methods an ensemble of c=-5 gravity graphs,
generated by coupling a conformal field theory with central charge c=-5 to
two-dimensional quantum gravity. We measure the fractal properties of the
ensemble, such as the string susceptibility exponent gamma_s and the intrinsic
fractal dimensions d_H. We find gamma_s = -1.5(1) and d_H = 3.36(4), in
reasonable agreement with theoretical predictions. In addition, we study the
critical behavior of an Ising model on a quenched ensemble of the c=-5 graphs
and show that it agrees, within numerical accuracy, with theoretical
predictions for the critical behavior of an Ising model coupled dynamically to
two-dimensional quantum gravity, provided the total central charge of the
matter sector is c=-5. From this we conjecture that the critical behavior of
the Ising model is determined solely by the average fractal properties of the
graphs, the coupling to the geometry not playing an important role.Comment: 23 pages, Latex, 7 figure
Blocking of Dynamical Triangulations with Matter
We use the recently proposed node decimation algorithm for blocking dynamical
geometries to investigate a class of models, with central charge greater than
unity, coupled to 2D gravity. We demonstrate that the blocking preserves the
fractal structure of the surfaces.Comment: Talk presented at LATTICE96(gravity), 3 pages, LaTeX, espcrc2.st
A real-space renormalization group for random surfaces
We propose a new real-space renormalization group transformation for dynamical triangulations. It is shown to preserve geometrical exponents such as the string susceptibility and Hausdorff dimension. We furthermore show evidence for a fixed point structure both in pure gravity and gravity coupled to a critical Ising system. In the latter case we are able to extract estimates for the gravitationally dressed exponents which agree to within 2-3% of the KPZ formula
4d Simplicial Quantum Gravity Interacting with Gauge Matter Fields
The effect of coupling non-compact gauge fields to four dimensional
simplicial quantum gravity is studied using strong coupling expansions and
Monte Carlo simulations. For one gauge field the back-reaction of the matter on
the geometry is weak. This changes, however, as more matter fields are
introduced. For more than two gauge fields the degeneracy of random manifolds
into branched polymers does not occur, and the branched polymer phase seems to
be replaced by a new phase with a negative string susceptibility exponent
and fractal dimension .Comment: latex2e, 10 pages incorporating 2 tables and 3 figures (using epsf
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
The Strong-Coupling Expansion in Simplicial Quantum Gravity
We construct the strong-coupling series in 4d simplicial quantum gravity up
to volume 38. It is used to calculate estimates for the string susceptibility
exponent gamma for various modifications of the theory. It provides a very
efficient way to get a first view of the phase structure of the models.Comment: LATTICE98(surfaces), 3 pages, 4 eps figure
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