R. L. Renken

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We establish the phase diagram of three–dimensional quantum gravity coupled to Ising matter. We find that in the negative curvature phase of the quantum gravity there is no disordered phase for ferromagnetic Ising matter because the coordination number of the sites diverges. In the positive curvature phase of the quantum gravity there is evidence for two(More)
By a sequence of numerical experiments we demonstrate that generic triangulations of the D−sphere forD > 3 contain one 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(More)
Non-compact lattice QED with two flavors of light dynamical quarks is simulated on 16 lattices, and the chiral condensate, monopole density and susceptibility and the meson masses are measured. Data from relatively high statistics runs at relatively small bare fermion masses of 0.005, 0.01, 0.02 and 0.03 (lattice units) are presented. Three independent(More)
We use Monte Carlo simulation to study the phase diagram of three-dimensional dynamical triangulations with a boundary. Three phases are indentified and characterized. One of these phases is a new, boundary dominated phase; a simple argument is presented to explain its existence. First-order transitions are shown to occur along the critical lines separating(More)
We study the XYmodel on a lattice with fluctuating connectivity. The expectation is that at an appropriate critical point such a system corresponds to a compactified boson coupled to 2d quantum gravity. Our simulations focus, in particular, on the important topological features of the system. The results lend strong support to the two phase structure(More)
The RP 2 gauge model which allows interpolation between the RP 2 and O(3) spin models is studied in 2D. We use Monte-Carlo renormalization techniques for blocking the mean spin-spin interaction, 〈A〉, and the mean gauge field plaquette, 〈P 〉. The presence of the O(3) renormalized trajectory is verified and is consistent with the known three-loop β-function.(More)