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

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

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

Two distinct types of neuronal asymmetries are controlled by the Caenorhabditis elegans zinc finger transcription factor die-1

Left/right asymmetric features of animals are either randomly distributed on either the left or right side within a population ("antisymmetries") or found stereotypically on one particular side of an animal ("directional asymmetries"). Both types of asymmetries can be found in nervous systems, but whether the regulatory programs that establish these asymmetries share any mechanistic features is not known. We describe here an unprecedented molecular link between these two types of asymmetries in Caenorhabditis elegans. The zinc finger transcription factor die-1 is expressed in a directionally asymmetric manner in the gustatory neuron pair ASE left (ASEL) and ASE right (ASER), while it is expressed in an antisymmetric manner in the olfactory neuron pair AWC left (AWCL) and AWC right (AWCR). Asymmetric die-1 expression is controlled in a fundamentally distinct manner in these two neuron pairs. Importantly, asymmetric die-1 expression controls the directionally asymmetric expression of gustatory receptor proteins in the ASE neurons and the antisymmetric expression of olfactory receptor proteins in the AWC neurons. These asymmetries serve to increase the ability of the animal to discriminate distinct chemosensory inputs

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

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

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

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

Spin Glasses on Thin Graphs

In a recent paper we found strong evidence from simulations that the Isingantiferromagnet on ``thin'' random graphs - Feynman diagrams - displayed amean-field spin glass transition. The intrinsic interest of considering such random graphs is that they give mean field results without long range interactions or the drawbacks, arising from boundary problems, of the Bethe lattice. In this paper we reprise the saddle point calculations for the Ising and Potts ferromagnet, antiferromagnet and spin glass on Feynman diagrams. We use standard results from bifurcation theory that enable us to treat an arbitrary number of replicas and any quenched bond distribution. We note the agreement between the ferromagnetic and spin glass transition temperatures thus calculated and those derived by analogy with the Bethe lattice, or in previous replica calculations. We then investigate numerically spin glasses with a plus or minus J bond distribution for the Ising and Q=3,4,10,50 state Potts models, paying particular attention to the independence of the spin glass transition from the fraction of positive and negative bonds in the Ising case and the qualitative form of the overlap distribution in all the models. The parallels with infinite range spin glass models in both the analytical calculations and simulations are pointed out.Comment: 13 pages of LaTex and 11 postscript figures bundled together with uufiles. Discussion of first order transitions for three or more replicas included and similarity to Ising replica magnet pointed out. Some additional reference

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