Ray L. Renken

Phase structure of four-dimensional simplicial quantum gravity

Abstract 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 of 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 peak.

Singular structure in 4D simplicial gravity

Abstract 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.

Numerical study of c > 1 matter coupled to quantum gravity☆

Abstract We present the results of a numerical simulation aimed at understanding the nature of the “c = 1 barrier” in two-dimensional quantum gravity. We study multiple Ising models living on dynamical φ3 graphs and analyse the behaviour of moments of the graph loop distribution. We note a universality at work as the average properties of typical graphs from the ensemble are determined only by the central charge. We further argue that the qualitative nature of these results can be understood from considering the effect of fluctuations about a mean field solution in the Ising sector.

Singular Vertices and the Triangulation Space of the D-sphere

Abstract By a sequence of numerical experiments we demonstrate that generic triangulations of the D -sphere for D > 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 also show a singular behaviour. Possible consequences for the DT model of four-dimensional quantum gravity are discussed.

Is there an exponential bound in four-dimensional simplicial gravity?

We have studied a model which has been proposed as a regularisation for four dimensional quantum gravity. The partition function is constructed by performing a weighted sum over all triangulations of the four sphere. Using numerical simulation we find that the number of such triangulations containing V simplices grows faster than exponentially with V . This property ensures that the model has no thermodynamic limit.

Entropy and the approach to the thermodynamic limit in three-dimensional simplicial gravity

Abstract 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 the number of nodes per unit volume show a slow power law approach to the infinite volume limit.

Spectroscopy, equation of state and monopole percolation in lattice QED with two flavors

Abstract Non-compact lattice QED with two flavors of light dynamical quarks is simulated on 164 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 methods of data analysis indicate that the critical point occurs at β = 0.225 (5) and that the monopole condensation and chiral symmetry breaking transitions are coincident. The monopole condensation data satisfies finite-size scaling hypotheses with critical indices compatible with four-dimensional percolation. The best chiral equation of state fit produces critical exponents (δ = 2.31, βmag = 0.763) which deviate significantly from mean field expectations. Data for the ratio of the sigma to pion masses produces an estimate of the critical index δ in good agreement with chiral condensate measurements. In the strong coupling phase the ratio of the meson masses are Mσ2/Mϱ2 ≈ 0.35, MA12/Mϱ2 ≈ 1.4 nd Mπ2/Mϱ2 ≈ 0.0, while on the weak coupling side of the transition Mπ2/Mϱ2 ≈ 1.0, MA12/Mϱ2 ≈ 1.0, indicating the restoration of chiral symmetry.

Thermodynamics of lattice QCD with two light quarks on a 16(3) x 8 lattice.

We have extended our earlier simulations of the high temperature behaviour of lattice QCD with two light flavours of staggered quarks on a

PHASE STRUCTURE OF DYNAMICAL TRIANGULATION MODELS IN THREE DIMENSIONS

16^3 \times 8

Hadron spectrum and matrix elements in QCD with dynamical Wilson fermions at 6/g2=5.3.

lattice to lower quark mass (m_q=0.00625). The transition from hadronic matter to a quark-gluon plasma is observed at