Searcharxiv⌕ Search

arXiv subjects

G. Thorleifsson

Publications and source records attributed to G. Thorleifsson.

34 records · Page 2Linked to original sources
arXiv1996

Simplicial Gravity in Dimension Greater than Two

We consider two issues in the DT model of quantum gravity. First, it is shown that the triangulation space for D>3 is dominated by triangulations containing a single singular (D-3)-simplex composed of vertices with divergent dual volumes. Second we study the ergodicity of current simulation algorithms. Results from runs conducted close to the phase transition of the four-dimensional theory are shown. We see no strong indications of ergodicity br eaking in the simulation and our data support recent claims that the transition is most probably first order. Furthermore, we show that the critical properties of the system are determined by the dynamics of remnant singular vertices.

hep-lat↗
arXiv1996

Spin-spin correlation functions of spin systems coupled to 2-d quantum gravity for $0 < c < 1$

We perform Monte Carlo simulations of 2-d dynamically triangulated surfaces coupled to Ising and three--states Potts model matter. By measuring spin-spin correlation functions as a function of the geodesic distance we provide substantial evidence for a diverging correlation length at $β_c$. The corresponding scaling exponents are directly related to the KPZ exponents of the matter fields as conjectured in [4] (NPB454(1995)313).

hep-lat↗
arXiv1996

Geometrical Interpretation of the KPZ Exponents

We provide evidence that the KPZ exponents in two-dimensional quantum gravity can be interpreted as scaling exponents of correlation functions which are functions of the invariant geodesic distance between the fields.

hep-lat↗
arXiv1996

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 $κ$. 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 $ν$ and the roughness exponent $ζ$. We also determine the critical exponents $η$ and $η_u$ describing the scale dependence of the bending rigidity ($κ(q) \sim q^{-η}$) and the induced elastic constants ($λ(q) \sim μ(q) \sim q^{η_u}$). At bending rigidity $κ= 1.1$, we find $ν= 0.95(5)$ (Hausdorff dimension $d_H = 2/ν= 2.1(1)$), $ζ= 0.64(2)$ and $η_u = 0.50(1)$. These results are consistent with the scaling relation $ζ= (2+η_u)/4$. The additional scaling relation $η= 2(1-ζ)$ implies $η= 0.72(4)$. A direct measurement of $η$ from the power-law decay of the normal-normal correlation function yields $η\approx 0.6$ on the $128^2$ lattice.

cond-mat↗
arXiv1995

Singular Vertices and the Triangulation Space of the D-sphere

By a sequence of numerical experiments we demonstrate that generic triangulations of the $D-$sphere for $D>3$ contain one {\it singular} $(D-3)-$simplex. The mean number of elementary $D-$simplices sharing this simplex increases with the volume of the triangulation according to a simple power law. The lower dimension subsimplices associated with this $(D-3)-$simplex also show a singular behaviour. Possible consequences for the DT model of four-dimensional quantum gravity are discussed.

hep-lat↗
arXiv1995

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.

hep-lat↗
arXiv1995

The Phase Diagram of Crystalline Surfaces

We report the status of a high-statistics Monte Carlo simulation of non-self-avoiding crystalline surfaces with extrinsic curvature on lattices of size up to $128^2$ nodes. We impose free boundary conditions. The free energy is a gaussian spring tethering potential together with a normal-normal bending energy. Particular emphasis is given to the behavior of the model in the cold phase where we measure the decay of the normal-normal correlation function.

hep-lat↗
arXiv1995

Baby Universes in 4d Dynamical Triangulation

We measure numerically the distribution of baby universes in the crumpled phase of the dynamical triangulation model of 4d quantum gravity. The relevance of the results to the issue of an exponential bound is discussed. The data are consistent with the existence of such a bound.

hep-lat↗
arXiv1995

Scaling and the Fractal Geometry of Two-Dimensional Quantum Gravity

We examine the scaling of geodesic correlation functions in two-dimensional gravity and in spin systems coupled to gravity. The numerical data support the scaling hypothesis and indicate that the quantum geometry develops a non-perturbative length scale. The existence of this length scale allows us to extract a Hausdorff dimension. In the case of pure gravity we find d_H approx. 3.8, in support of recent theoretical calculations that d_H = 4. We also discuss the back-reaction of matter on the geometry.

hep-lat↗
arXiv1994

Level Crossing for Hot Sphalerons

We study the spectrum of the Dirac Hamiltonian in the presence of high temperature sphaleron-like fluctuations of the electroweak gauge and Higgs fields, relevant for the conditions prevailing in the early universe. The fluctuations are created by numerical lattice simulations. It is shown that a change in Chern-Simons number by one unit is accompanied by eigenvalues crossing zero and a change of sign of the generalized chirality $\tGf= (-1)^{2T+1} \gf$ which labels these modes. This provides further evidence that the sphaleron-like configurations observed in lattice simulations may be viewed as representing continuum configurations.

hep-lat↗
arXiv1993

A Universal Fractal Structure of 2D Quantum Gravity for c > 1

We investigate the fractal structure of $2d$ quantum gravity coupled to matter by measuring the distributions of so-called baby universes. We demonstrate that the method works well as long as $c \leq 1$. For $c >1$ it is not clear what distribution to expect. However, we observe strikingly similar distributions for various kinds of matter fields with the same $c$. This indicate that there might be some range of $c >1$ where the central charge of the matter fields alone determines the fractal structure of gravity coupled to matter. The hypothesis that the string susceptibility $\g = 1/3$ is found to be compatible with the data for $1 < c \leq 4$.

hep-th↗
arXiv1993

A Universal Fractal Structure of 2D Quantum Gravity for c > 1

We investigate the fractal structure of $2d$ quantum gravity coupled to matter by measuring the distributions of so-called baby universes. We demonstrate that the method works well as long as $c \leq 1$. For $c >1$ it is not clear what distribution to expect. However, we observe strikingly similar distributions for various kinds of matter fields with the same $c$. This indicate that there might be some range of $c >1$ where the central charge of the matter fields alone determines the fractal structure of gravity coupled to matter. The hypothesis that the string susceptibility $\g = 1/3$ is found to be compatible with the data for $1 < c \leq 4$.

hep-lat↗
arXiv1993

Baby universes in 2d quantum gravity

We investigate the fractal structure of $2d$ quantum gravity, both for pure gravity and for gravity coupled to multiple gaussian fields and for gravity coupled to Ising spins. The roughness of the surfaces is described in terms of baby universes and using numerical simulations we measure their distribution which is related to the string susceptibility exponent $\g_{string}$.

hep-th↗
arXiv1992

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.

hep-th↗
arXiv1992

Matter fields with c > 1 coupled to 2d gravity

We solve a class of branched polymer models coupled to spin systems and show that they have no phase transition and are either always magnetized or never magnetized depending on the branching weights. By comparing these results with numerical simulations of two-dimensional quantum gravity coupled to matter fields with central charge $c$ we provide evidence that for $c$ sufficiently large ($c\geq 12$) these models are effectively described by branched polymers. Moreover, the numerical results indicate a remarkable universality in the influence on the geometry of surfaces due to the interaction with matter. For spin systems this influence only depends on the total central charge.

hep-th↗