3 research outputs found
Simulations of Dynamically Triangulated Gravity -- an Algorithm for Arbitrary Dimension
Recent models for discrete euclidean quantum gravity incorporate a sum over
simplicial triangulations. We describe an algorithm for simulating such models
in general dimensions. As illustration we show results from simulations in four
dimensionsComment: 14 pages, 6 figures, CERN-TH.7286/9
Failure of the Regge approach in two dimensional quantum gravity
Regge's method for regularizing euclidean quantum gravity is applied to two
dimensional gravity. We use two different strategies to simulate the Regge path
integral at a fixed value of the total area: A standard Metropolis simulation
combined with a histogramming method and a direct simulation using a Hybrid
Monte Carlo algorithm. Using topologies with genus zero and two and a scale
invariant integration measure, we show that the Regge method does not reproduce
the value of the string susceptibility of the continuum model. We show that the
string susceptibility depends strongly on the choice of the measure in the path
integral. We argue that the failure of the Regge approach is due to spurious
contributions of reparametrization degrees of freedom to the path integral.Comment: 27 pages, LaTex + uuencoded figure files (13 postscript files
Multigrid Methods in Lattice Field Computations
The multigrid methodology is reviewed. By integrating numerical processes at
all scales of a problem, it seeks to perform various computational tasks at a
cost that rises as slowly as possible as a function of , the number of
degrees of freedom in the problem. Current and potential benefits for lattice
field computations are outlined. They include: solution of Dirac
equations; just operations in updating the solution (upon any local
change of data, including the gauge field); similar efficiency in gauge fixing
and updating; operations in updating the inverse matrix and in
calculating the change in the logarithm of its determinant; operations
per producing each independent configuration in statistical simulations
(eliminating CSD), and, more important, effectively just operations per
each independent measurement (eliminating the volume factor as well). These
potential capabilities have been demonstrated on simple model problems.
Extensions to real life are explored.Comment: 4