Alain Billoire

SCALING PROPERTIES OF RANDOMLY TRIANGULATED PLANAR RANDOM SURFACES: A numerical study

Results of Monte Carlo simulations of a model of random surfaces based on planar random triangulations with gaussian embedding in D-dimensional euclidean space are presented, for various positive and negative values of D and various forms for the action. Estimates are given for the fractal dimension (Hausdorff dimension of the embedding) and the spreading dimension (intrinsic Hausdorff dimension). The scaling properties appear to depend on the short-distance properties of the triangulations and seem to be nonuniversal, at least for positive D.

Correlations between adjoint polyakov loops

Abstract We consider 4D SU(2) lattice gauge theory and report a high statistics MC investigation of correlations between Polyakov loops in the adjoint SU(2) representation. For large β-values and on lattices with small sized spatial volumes these correlations allow glueball estimates improving results of the literature by several orders of magnitude. Our data for the mass gap and the string tension exhibit a very sharp crossover between the small-volume limit and the infinite-volume limit. This is prohibitive to extracting physics from Luschers weak coupling expansion by matching it with numerical data.

Markov Chain Monte Carlo Simulations

Markov Chain Monte Carlo (MCMC) simulations are widely used in many branches of science. We explain the basic method and illustrate it for a simple statistical physics system, the Ising ferromagnet in two dimensions An overview of MCMC updating scheme is subsequently given. The final section of this article focuses on so called generalized ensemble algorithms. Keywords: Monte Carlo method; Markov chain; Ising ferromagnet; Metropolis algorithm; Boltzmann–Gibbs ensemble

Excited glueball states in four-dimensional SU(3) lattice gauge theory

Abstract For SU( N ) ( N ⩾ 2) lattice gauge theories in four dimensions we construct all irreducible representations of the full cubic group on spacelike Wilson loop operators up to length 6. Relying on this set of operators preliminary Monte Carlo results for SU(3) excited glueball states are reported.

Observation of FSS for a first-order phase transition

Abstract We present the results of a multicanonical simulation of the q = 20 two-dimensional Potts model in the transition region. This is a very strong first-order phase transition. We observe, for the first time, the asymptotic finite size scaling behavior predicted by Borgs and Kotecký close to a first-order phase transition point.

A Determination of interface free energies

Abstract We determine the interface free energy Fo.d. between disordered and ordered phases in the q = 10 and q = 20 2d Potts models using the results of multicanonical Monte Carlo simulations on L2 lattices, and suitable finite-volume estimators. Our results, when extrapolated to the finite-volume limit, agree to high precision with recent analytical calculations. At the transition point βt the probability distribution function of the energy exhibits two maxima. Their locations have 1/L2 corrections, in contradiction with claims of 1/L behavior made in the literature. Our data show a flat region in between the two maxima which characterizes two domain configurations.

A Monte Carlo Simulation of Random Surfaces

Abstract We use a previously proposed stochastic process and carry out Monte Carlo simulations for two models of random surfaces defined on hypercubic lattices. Tests are carried out in five dimensions. The critical coupling constants are estimated for both models. One of the models allows also results on its entropy.

SU(2) lattice gauge theory: Standard action versus Symanzik's tree-improved action

We carry out Monte Carlo simulations of the 4d SU(2) lattice gauge theory. The standard action and the Symanzik tree-improved action are used. Results for the string tension, glueball masses, and energy-momentum dispersion are reported. In case of the standard action our results are a finite size study extending previous investigations.

Spin-glass overlap barriers in three and four dimensions

For the Edwards-Anderson Ising spin-glass model in three and four dimensions (3d and 4d) we have performed high statistics Monte Carlo calculations of those free-energy barriers

Hadronic spectroscopy in lattice QCD with dynamical staggered quark loops

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