503 research outputs found
The Concept of Time in 2D Quantum Gravity
We show that the ``time'' t_s defined via spin clusters in the Ising model
coupled to 2d gravity leads to a fractal dimension d_h(s) = 6 of space-time at
the critical point, as advocated by Ishibashi and Kawai. In the unmagnetized
phase, however, this definition of Hausdorff dimension breaks down. Numerical
measurements are consistent with these results. The same definition leads to
d_h(s)=16 at the critical point when applied to flat space. The fractal
dimension d_h(s) is in disagreement with both analytical prediction and
numerical determination of the fractal dimension d_h(g), which is based on the
use of the geodesic distance t_g as ``proper time''. There seems to be no
simple relation of the kind t_s = t_g^{d_h(g)/d_h(s)}, as expected by
dimensional reasons.Comment: 14 pages, LaTeX, 2 ps-figure
4D Quantum Gravity Coupled to Matter
We investigate the phase structure of four-dimensional quantum gravity
coupled to Ising spins or Gaussian scalar fields by means of numerical
simulations.
The quantum gravity part is modelled by the summation over random simplicial
manifolds, and the matter fields are located in the center of the 4-simplices,
which constitute the building blocks of the manifolds. We find that the
coupling between spin and geometry is weak away from the critical point of the
Ising model. At the critical point there is clear coupling, which qualitatively
agrees with that of gaussian fields coupled to gravity. In the case of pure
gravity a transition between a phase with highly connected geometry and a phase
with very ``dilute'' geometry has been observed earlier. The nature of this
transition seems unaltered when matter fields are included.
It was the hope that continuum physics could be extracted at the transition
between the two types of geometries. The coupling to matter fields, at least in
the form discussed in this paper, seems not to improve the scaling of the
curvature at the transition point.Comment: 15 pages, 9 figures (available as PS-files by request). Late
Order parameters in spin-spin and plaquette lattice theories
We present some basic properties of the gauge theories in the lattice formulation. We discuss the possible order parameters of the theory and their usefulness from the point of view of the numerical calculations. We study the properties of the low coupling constant expansion, i.e. the continuum limit of the theory. Finally we show the results of the numerical calculations for various lattice systems
Random walks on combs
We develop techniques to obtain rigorous bounds on the behaviour of random
walks on combs. Using these bounds we calculate exactly the spectral dimension
of random combs with infinite teeth at random positions or teeth with random
but finite length. We also calculate exactly the spectral dimension of some
fixed non-translationally invariant combs. We relate the spectral dimension to
the critical exponent of the mass of the two-point function for random walks on
random combs, and compute mean displacements as a function of walk duration. We
prove that the mean first passage time is generally infinite for combs with
anomalous spectral dimension.Comment: 42 pages, 4 figure
Lattice Gauge Theory -- Present Status
Lattice gauge theory is our primary tool for the study of non-perturbative
phenomena in hadronic physics. In addition to giving quantitative information
on confinement, the approach is yielding first principles calculations of
hadronic spectra and matrix elements. After years of confusion, there has been
significant recent progress in understanding issues of chiral symmetry on the
lattice. (Talk presented at HADRON 93, Como, Italy, June 1993.)Comment: 11 pages, BNL-4946
A new perspective on matter coupling in 2d quantum gravity
We provide compelling evidence that a previously introduced model of
non-perturbative 2d Lorentzian quantum gravity exhibits (two-dimensional)
flat-space behaviour when coupled to Ising spins. The evidence comes from both
a high-temperature expansion and from Monte Carlo simulations of the combined
gravity-matter system. This weak-coupling behaviour lends further support to
the conclusion that the Lorentzian model is a genuine alternative to Liouville
quantum gravity in two dimensions, with a different, and much `smoother'
critical behaviour.Comment: 24 pages, 7 figures (postscript
Grand-Canonical Ensemble of Random Surfaces with Four Species of Ising Spins
The grand-canonical ensemble of dynamically triangulated surfaces coupled to
four species of Ising spins (c=2) is simulated on a computer. The effective
string susceptibility exponent for lattices with up to 1000 vertices is found
to be . A specific scenario for models is
conjectured.Comment: LaTeX, 11 pages + 1 postscript figure appended, preprint LPTHE-Orsay
94/1
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
Smooth Random Surfaces from Tight Immersions?
We investigate actions for dynamically triangulated random surfaces that
consist of a gaussian or area term plus the {\it modulus} of the gaussian
curvature and compare their behavior with both gaussian plus extrinsic
curvature and ``Steiner'' actions.Comment: 7 page
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