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 $c \leq 1$, 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

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

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

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

The Flat Phase of Crystalline Membranes

We present the results of a high-statistics Monte Carlo simulation of a phantom crystalline (fixed-connectivity) membrane with free boundary. We verify the existence of a flat phase by examining lattices of size up to $128^2$. The Hamiltonian of the model is the sum of a simple spring pair potential, with no hard-core repulsion, and bending energy. The only free parameter is the the bending rigidity $\kappa$. In-plane elastic constants are not explicitly introduced. We obtain the remarkable result that this simple model dynamically generates the elastic constants required to stabilise the flat phase. We present measurements of the size (Flory) exponent $\nu$ and the roughness exponent $\zeta$. We also determine the critical exponents $\eta$ and $\eta_u$ describing the scale dependence of the bending rigidity ($\kappa(q) \sim q^{-\eta}$) and the induced elastic constants ($\lambda(q) \sim \mu(q) \sim q^{\eta_u}$). At bending rigidity $\kappa = 1.1$, we find $\nu = 0.95(5)$ (Hausdorff dimension $d_H = 2/\nu = 2.1(1)$), $\zeta = 0.64(2)$ and $\eta_u = 0.50(1)$. These results are consistent with the scaling relation $\zeta = (2+\eta_u)/4$. The additional scaling relation $\eta = 2(1-\zeta)$ implies $\eta = 0.72(4)$. A direct measurement of $\eta$ from the power-law decay of the normal-normal correlation function yields $\eta \approx 0.6$ on the $128^2$ lattice.Comment: Latex, 31 Pages with 14 figures. Improved introduction, appendix A and discussion of numerical methods. Some references added. Revised version to appear in J. Phys.

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 $U(1)$ 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 $\gamma$ and fractal dimension $d_H \approx 4$.Comment: latex2e, 10 pages incorporating 2 tables and 3 figures (using epsf