1,170 research outputs found
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
Universality theorems for inscribed polytopes and Delaunay triangulations
We prove that every primary basic semialgebraic set is homotopy equivalent to
the set of inscribed realizations (up to M\"obius transformation) of a
polytope. If the semialgebraic set is moreover open, then, in addition, we
prove that (up to homotopy) it is a retract of the realization space of some
inscribed neighborly (and simplicial) polytope. We also show that all algebraic
extensions of are needed to coordinatize inscribed polytopes.
These statements show that inscribed polytopes exhibit the Mn\"ev universality
phenomenon.
Via stereographic projections, these theorems have a direct translation to
universality theorems for Delaunay subdivisions. In particular, our results
imply that the realizability problem for Delaunay triangulations is
polynomially equivalent to the existential theory of the reals.Comment: 15 pages, 2 figure
On the Universality of Matrix Models for Random Surfaces
We present an alternative procedure to eliminate irregular contributions in
the perturbation expansion of c=0-matrix models representing the sum over
triangulations of random surfaces, thereby reproducing the results of Tutte [1]
and Brezin et al. [2] for the planar model. The advantage of this method is
that the universality of the critical exponents can be proven from general
features of the model alone without explicit determination of the free energy
and therefore allows for several straightforward generalizations including
cases with non-vanishing central charge c< 1.Comment: 9 pages, 3 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
Minimal Dynamical Triangulations of Random Surfaces
We introduce and investigate numerically a minimal class of dynamical
triangulations of two-dimensional gravity on the sphere in which only vertices
of order five, six or seven are permitted. We show firstly that this
restriction of the local coordination number, or equivalently intrinsic scalar
curvature, leaves intact the fractal structure characteristic of generic
dynamically triangulated random surfaces. Furthermore the Ising model coupled
to minimal two-dimensional gravity still possesses a continuous phase
transition. The critical exponents of this transition correspond to the usual
KPZ exponents associated with coupling a central charge c=1/2 model to
two-dimensional gravity.Comment: Latex, 9 pages, 3 figures, Published versio
Locally Causal Dynamical Triangulations in Two Dimensions
We analyze the universal properties of a new two-dimensional quantum gravity
model defined in terms of Locally Causal Dynamical Triangulations (LCDT).
Measuring the Hausdorff and spectral dimensions of the dynamical geometrical
ensemble, we find numerical evidence that the continuum limit of the model lies
in a new universality class of two-dimensional quantum gravity theories,
inequivalent to both Euclidean and Causal Dynamical Triangulations
The 3d Ising Model represented as Random Surfaces
We consider a random surface representation of the three-dimensional Ising
model.The model exhibit scaling behaviour and a new critical index \k which
relates \g_{string} for the bosonic string to the exponent \a of the
specific heat of the 3d Ising model is introduced. We try to determine \k by
numerical simulations.Comment: No figures included. Available by ordinary mail on request. 13 pages.
Latex. preprint NBI-HE-92-8
- …