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.Comment: 15 pages, 9 figure

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.Comment: 8 pages, 4 figure

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.Comment: Talk presented at LATTICE96(gravity

Singular Structure in 4D Simplicial Gravity

We show that the phase transition previously observed in dynamical triangulation models of quantum gravity can be understood as being due to the creation of a singular link. The transition between singular and non-singular geometries as the gravitational coupling is varied appears to be first order.Comment: 9 pages, 5 figures, 3 references adde

Phase Structure of Four Dimensional Simplicial Quantum Gravity

We present the results of a high statistics Monte Carlo study of a model for four dimensional euclidean quantum gravity based on summing over triangulations. We show evidence for two phases; in one there is a logarithmic scaling on the mean linear extent with volume, whilst the other exhibits power law behaviour with exponent 1/2. We are able to extract a finite size scaling exponent governing the growth of the susceptibility peakComment: 11 pages (5 figures

Thermal phases of D1-branes on a circle from lattice super Yang-Mills

We report on the results of numerical simulations of 1+1 dimensional SU(N) Yang-Mills theory with maximal supersymmetry at finite temperature and compactified on a circle. For large N this system is thought to provide a dual description of the decoupling limit of N coincident D1-branes on a circle. It has been proposed that at large N there is a phase transition at strong coupling related to the Gregory-Laflamme (GL) phase transition in the holographic gravity dual. In a high temperature limit there was argued to be a deconfinement transition associated to the spatial Polyakov loop, and it has been proposed that this is the continuation of the strong coupling GL transition. Investigating the theory on the lattice for SU(3) and SU(4) and studying the time and space Polyakov loops we find evidence supporting this. In particular at strong coupling we see the transition has the parametric dependence on coupling predicted by gravity. We estimate the GL phase transition temperature from the lattice data which, interestingly, is not yet known directly in the gravity dual. Fine tuning in the lattice theory is avoided by the use of a lattice action with exact supersymmetry.Comment: 21 pages, 8 figures. v2: References added, two figures were modified for clarity. v3: Normalisation of lattice coupling corrected by factor of two resulting in change of estimate for c_cri

Absence of sign problem in two-dimensional N=(2,2) super Yang-Mills on lattice

We show that N=(2,2) SU(N) super Yang-Mills theory on lattice does not have sign problem in the continuum limit, that is, under the phase-quenched simulation phase of the determinant localizes to 1 and hence the phase-quench approximation becomes exact. Among several formulations, we study models by Cohen-Kaplan-Katz-Unsal (CKKU) and by Sugino. We confirm that the sign problem is absent in both models and that they converge to the identical continuum limit without fine tuning. We provide a simple explanation why previous works by other authors, which claim an existence of the sign problem, do not capture the continuum physics.Comment: 27 pages, 24 figures; v2: comments and references added; v3: figures on U(1) mass independence and references added, to appear in JHE

Gauged O(n) spin models in one dimension

We consider a gauged O(n) spin model, n >= 2, in one dimension which contains both the pure O(n) and RP(n-1) models and which interpolates between them. We show that this model is equivalent to the non-interacting sum of the O(n) and Ising models. We derive the mass spectrum that scales in the continuum limit, and demonstrate that there are two universality classes, one of which contains the O(n) and RP(n-1) models and the other which has a tuneable parameter but which is degenerate in the sense that it arises from the direct sum of the O(n) and Ising models.Comment: 9 pages, no figures, LaTeX sourc

Impact of dredging on the volute Cymbiolacca pulchra and its environment at Heron Island, Great Barrier Reef, Australia

The impact of dredging operations on the volute Gastropod (Cymbiolacca pulchra) population of a coral reef atoll (Heron Island, Great Barrier Reef, Australia) was investigated using data from annual surveys of the population and its environment Comparisons were made of pre-dredging (1984 to 1986), during-dredging (1987) and post-dredging (1988 and 1989) summer densities and size distributions of volutes at eight locations on the reef. There was significant variation among the sites in the pre-dredging years with volutes restricted to four sites characterised by a combination ofre1ative1y low bommie cover « 2%) and high sand cover (> 75%). All four sites were influenced by the dredge plume during dredging operations (September to November 1987 and February 1988). Volute densities declined significantly during dredging (1987) compared to the pre-dredging years. In the following year (1988) the difference was highly significant with zero densities recorded. By 1989 there had been a recovery with no significant difference in the overall density of volutes although the density of small volutes was greater and larger volutes smaller compared to pre-dredging densities. From June 1985 to May 1986 monthly counts were made at all sites to examine seasonal patterns of recruitment Recruitment into the population occurred over much of the year, though it tended to be higher in the autumn months (March to May), presumably following summer breeding. We suggest that the declines in volute densities were probably due to a failure of recruitment during dredging coupled with a loss of large volutes which may have resulted from natural mortality, emigration, or dredging. The recovery probably followed immigration of large volutes from less affected areas. The environmental factors of percent cover of sand, rock, rubble, coral, bommies and macroalgae were also monitored and there were significant changes in the cover of algae, coral, sand and rubble. These changes are interpreted as covariates rather than causes of observed changes in volute densities. Post-dredging increases in the cover of algae persisted beyond the termination of this study

Entropy and the Approach to the Thermodynamic Limit in Three-Dimensional Simplicial Gravity

We present numerical results supporting the existence of an exponential bound in the dynamical triangulation model of three-dimensional quantum gravity.Both the critical coupling and various other quantities show a slow power law approach to the infinite volume limit