1,916 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
Suppressing Curvature Fluctuations in Dynamical Triangulations
We study numerically the dynamical triangulation formulation of
two-dimensional quantum gravity using a restricted class of triangulation,
so-called minimal triangulations, in which only vertices of coordination number
5, 6, and 7 are allowed. A real-space RG analysis shows that for pure gravity
(central charge c = 0) this restriction does not affect the critical behavior
of the model. Furthermore, we show that the critical behavior of an Ising model
coupled to minimal dynamical triangulations (c = 1/2) is still governed by the
KPZ-exponents.Comment: Talk presented at LATTICE96(gravity), 3 pages, LaTeX, espcrc2.sty, 1
figur
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
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
Anisotropic Membranes
We describe the statistical behavior of anisotropic crystalline membranes. In
particular we give the phase diagram and critical exponents for phantom
membranes and discuss the generalization to self-avoiding membranes.Comment: LATTICE98(surfaces) 5 pages, 4 Postscript figure
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
The Poisson ratio of crystalline surfaces
A remarkable theoretical prediction for a crystalline (polymerized) surface
is that its Poisson ratio (\sigma) is negative. Using a large scale Monte Carlo
simulation of a simple model of such surfaces we show that this is indeed true.
The precise numerical value we find is (\sigma \simeq -0.32) on a (128^2)
lattice at bending rigidity (kappa = 1.1). This is in excellent agreement with
the prediction (\sigma = -1/3) following from the self-consistent screening
approximation of Le Doussal and Radzihovsky.Comment: 7 pages, 2 EPS figures, LaTeX2e. Revised version accepted for
publication on Europhys. Let
Monte Carlo Renormalization of 2d Simplicial Quantum Gravity Coupled to Gaussian Matter
We extend a recently proposed real-space renormalization group scheme for
dynamical triangulations to situations where the lattice is coupled to
continuous scalar fields. Using Monte Carlo simulations in combination with a
linear, stochastic blocking scheme for the scalar fields we are able to
determine the leading eigenvalues of the stability matrix with good accuracy
both for c = 1 and c = 10 theories.Comment: 17 pages, 7 figure
Besov's Type Embedding Theorem for Bilateral Grand Lebesgue Spaces
In this paper we obtain the non-asymptotic norm estimations of Besov's type
between the norms of a functions in different Bilateral Grand Lebesgue spaces
(BGLS). We also give some examples to show the sharpness of these inequalities
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