Clive F. Baillie

Crumpling in dynamically triangulated random surfaces with extrinsic curvature

Abstract We present the results of a numerical simulation of dynamically triangulated random surfaces of fixed topology with extrinsic curvature. We use two different discretizations of the extrinsic curvature and observe the differing nature of the crumpling transitions and smooth phases. The effect of the extrinsic curvature on both the extrinsic and intrinsic geometry of the model is examined in three and four dimensions. We also discuss the similarities between our simulation and those of surfaces of fixed triangulation and consider the connection between models with extrinsic curvature and superstrings.

Multiple Potts models coupled to two-dimensional quantum gravity

Abstract We perform Monte Carlo simulations using the Wolff cluster algorithm of 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.

Cluster identification algorithms for spin models—sequential and parallel

Monte Carlo cluster update algorithms are extremely efficient for simulating spin models near their phase transitions, where local update algorithms suffer severe critical slowing down. Unfortunately, as the cluster algorithms are highly irregular as well as nonlocal, they are much more difficult to parallelize efficiently. The main difficulty lies in identifying which spins belong to which cluster. In this paper we investigate a number of cluster identification algorithms, both sequential and parallel, which we have implemented on serial, SIMD and MIMD computers.

Benchmarking advanced architecture computers

Recently, a number of advanced architecture machines have become commercially available. These new machines promise better cost performance than traditional computers, and some of them have the potential of competing with current supercomputers, such as the CRAY X-MP, in terms of maximum performance. This paper describes the methodology and results of a pilot study of the performance of a broad range of advanced architecture computers using a number of complete scientific application programs. The computers evaluated include: 1shared-memory bus architecture machines such as the Alliant FX/8, the Encore Multimax, and the Sequent Balance and Symmetry 2shared-memory network-connected machines such as the Butterfly 3distributed-memory machines such as the NCUBE, Intel and Jet Propulsion Laboratory (JPL)/Caltech hypercubes 4very long instruction word machines such as the Cydrome Cydra-5 5SIMD machines such as the Connection Machine 6‘traditional’ supercomputers such as the CRAY X-MP, CRAY-2 and SCS-40. Seven application codes from a number of scientific disciplines have been used in the study, although not all the codes were run on every machine. The methodology and guidelines for establishing a standard set of benchmark programs for advanced architecture computers are discussed. The CRAYs offer the best performance on the benchmark suite; the shared memory multiprocessor machines generally permitted some parallelism, and when coupled with substantial floating point capabilities (as in the Alliant FX/8 and Sequent Symmetry), provided an order of magnitude less speed than the CRAYs. Likewise, the early generation hypercubes studied here generally ran slower than the CRAYs, but permitted substantial parallelism from each of the application codes.

Further investigations of the crumpling transition in dynamically triangulated random surfaces

Abstract We examine further the critical behaviour of dynamically triangulated random surfaces (DTRS) with extrinsic curvature at their second-order crumpling transition. We show that the string tension in these models may be scaling near the transition in such a way that the physical string tension is finite, unlike models containing only a Polyakov term, suggesting that one can use DTRS as a discretization of subcritical string theory. We explore the universality properties of DTRS, showing that an apparently irrelevant term can affect the phase transition. We also find that the observed phase transition persists when the surfaces are embedded in higher dimensions, contradicting the naive expectations of a saddle point expansion.

Quenching 2D quantum gravity

Abstract We simulate the Ising model on a set of fixed random o 3 graphs, which corresponds to a 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 o 3 graphs, flat lattices and a single fixed o 3 graph.

QCD with dynamical Wilson fermions. II.

We present results for the QCD spectrum and the matrix elements of scalar and axial-vector densities at β=6/g2=5.4, 5.5, 5.6. The lattice update was done using the hybrid Monte Carlo algorithm to include two flavors of dynamical Wilson fermions. We have explored quark masses in the range ms≤mq≤3ms. The results for the spectrum are similar to quenched simulations and mass ratios are consistent with phenomenological heavy-quark models. The results for matrix elements of the scalar density show that the contribution of sea quarks is comparable to that of the valence quarks. This has important implications for the pion-nucleon σ term.

Steiner variations on random surfaces

Abstract 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.

Softening of first-order phase transition on quenched random gravity graphs

Abstract We perform extensive Monte Carlo simulations of the 10-state Potts model on quenched two-dimensional Φ 3 gravity graphs to study the effect of quenched coordination number randomness on the nature of 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, representing presumably a new universality class. This result is in striking contrast to a recent Monte Carlo study of the 8-state Potts model on two-dimensional Poissonian random lattices of Voronoi/Delaunay type, where the phase transition clearly stayed of first order, but is in qualitative agreement with results for quenched bond randomness on regular lattices. A precedent for such softening with connectivity disorder is known: in the 10-state Potts model on annealed Φ 3 gravity graphs a continuous transition is also observed.

Scaling in Steiner random surfaces

It has been suggested that the modified Steiner action functional has desirble 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.