Steiner Variations on Random Surfaces

Ambartzumian et.al. suggested that the modified Steiner action functional had desirable properties for a random surface action. However, Durhuus and Jonsson pointed out that such an action led to an ill-defined grand-canonical partition function and suggested that the addition of an area term might improve matters. In this paper we investigate this and other related actions numerically for dynamically triangulated random surfaces and compare the results with the gaussian plus extrinsic curvature actions that have been used previously.Comment: 8 page

Scaling in Steiner Random Surfaces

It has been suggested that the modified Steiner action functional has desirable properties for a random surface action. In this paper we investigate the scaling of the string tension and massgap in a variant of this action on dynamically triangulated random surfaces and compare the results with the gaussian plus extrinsic curvature actions that have been used previously.Comment: 7 pages, COLO-HEP-32

Multiple Potts Models Coupled to Two-Dimensional Quantum Gravity

We perform Monte Carlo simulations using the Wolff cluster algorithm of {\it multiple} $q=2,3,4$ state Potts models on dynamical phi-cubed graphs of spherical topology in order to investigate the $c>1$ region of two-dimensional quantum gravity. Contrary to naive expectation we find no obvious signs of pathological behaviour for $c>1$. We discuss the results in the light of suggestions that have been made for a modified DDK ansatz for $c>1$.Comment: 9 page

Dgsos on DTRS

We perform simulations of a discrete gaussian solid on solid (DGSOS) model on dynamical $\phi^3$ graphs, which is equivalent to coupling the model to 2d quantum gravity, using the cluster algorithms recently developed by Evertz et.al.for use on fixed lattices. We find evidence from the growth of the width-squared in the rough phase of KT-like behaviour, which is consistent with theoretical expectations. We also investigate the cluster statistics, dynamical critical exponent and lattice properties, and compare these with the dual XY model.Comment: 9 pages, COLO-HEP-32

Spin Models on Thin Graphs

We discuss the utility of analytical and numerical investigation of spin models, in particular spin glasses, on ordinary ``thin'' random graphs (in effect Feynman diagrams) using methods borrowed from the ``fat'' graphs of two dimensional gravity. We highlight the similarity with Bethe lattice calculations and the advantages of the thin graph approach both analytically and numerically for investigating mean field results.Comment: Contribution to Parallel Session at Lattice95, 4 pages. Dodgy compressed ps file replaced with uuencoded LaTex original + ps figure

3d quantum gravity coupled to matter

We investigate the phase structure of three-dimensional quantum gravity coupled to an Ising spin system by means of numerical simulations. The quantum gravity part is modelled by the summation over random simplicial manifolds, and the Ising spins are located in the center of the tetrahedra, which constitute the building blocks of the piecewise linear manifold. We find that the coupling between spin and geometry is weak away from the critical point of the Ising model. At the critical point there is clear coupling, which however does not seem to change the first order transition between the ``hot'' and ``cold'' phase of three dimensional simplicial quantum gravity observed earlier.Comment: 10 pages, nbi-he-92-31 six figures available as postscript files by reques

Damaging 2D Quantum Gravity

We investigate numerically the behaviour of damage spreading in a Kauffman cellular automaton with quenched rules on a dynamical $\phi^3$ graph, which is equivalent to coupling the model to discretized 2D gravity. The model is interesting from the cellular automaton point of view as it lies midway between a fully quenched automaton with fixed rules and fixed connectivity and a (soluble) fully annealed automaton with varying rules and varying connectivity. In addition, we simulate the automaton on a fixed $\phi^3$ graph coming from a 2D gravity simulation as a means of exploring the graph geometry.Comment: 6 pages, COLO-HEP-332;LPTHE-Orsay-93-5

Square Gravity

We simulate the Ising model on dynamical quadrangulations using a generalization of the flip move for triangulations with two aims: firstly, as a confirmation of the universality of the KPZ/DDK exponents of the Ising phase transition, worthwhile in view of some recent surprises with other sorts of dynamical lattices; secondly, to investigate the transition of the Ising antiferromagnet on a dynamical loosely packed (bipartite) lattice. In the latter case we show that it is still possible to define a staggered magnetization and observe the antiferromagnetic analogue of the transition.Comment: LaTeX file and 7 postscript figures bundled together with uufile

Quenching 2D Quantum Gravity

We simulate the Ising model on a set of fixed random $\phi^3$ graphs, which corresponds to a {\it quenched} coupling to 2D gravity rather than the annealed coupling that is usually considered. We investigate the critical exponents in such a quenched ensemble and compare them with measurements on dynamical $\phi^3$ graphs, flat lattices and a single fixed $\phi^3$ graph.Comment: 8 page

Softening Transitions with Quenched 2D Gravity

We perform extensive Monte Carlo simulations of the 10-state Potts model on quenched two-dimensional $\Phi^3$ gravity graphs to study the effect of quenched connectivity disorder on the phase transition, which is strongly first order on regular lattices. The numerical data provides strong evidence that, due to the quenched randomness, the discontinuous first-order phase transition of the pure model is softened to a continuous transition.Comment: 3 pages, LaTeX + 1 postscript figure. Talk presented at LATTICE96(other models). See also http://www.cond-mat.physik.uni-mainz.de/~janke/doc/home_janke.htm