Monte Carlo Algorithms For Reduced Lattices, Mixed Actions, And Double-Trace Deformations

Abstract

We construct efficient Monte Carlo updating algorithms for two classes of pure SU(N) lattice gauge actions with non-linear dependence on the link variables. Our construction generalises the method of auxiliary variables used by Fabricius and Haan in the framework of Eguchi-Kawai models. We first review the original Fabricius-Haan method of constructing a pseudo-heatbath algorithm for fully reduced models, and discuss its extension to lattices with any number of reduced directions. We then use a similar method to construct updating algorithms for generic SU(N) mixed Wilson actions. We construct explicit examples of algorithms for Wilson actions whose plaquettes are in an irreducible representation of SU(N) with N-ality up to 3. We also construct updating algorithms for the lattice version of centre-stabilised SU(N) Yang-Mills theories defined on R^{d-1} x S^1, including the case of a fully reduced compact direction. We simulate the new algorithms and show that they are, in general, significantly more efficient than their Metropolis counterparts.

51 pages, 19 figures

References in corpus (4)

• Center-stabilized Yang-Mills theory: confinement and large $N$ volume independence
• Volume independence in large Nc QCD-like gauge theories
• Does the crossover from perturbative to nonperturbative physics in QCD become a phase transition at infinite N ?
• Biased Metropolis-Heat-Bath Algorithm for Fundamental-Adjoint SU(2) Lattice Gauge Theory

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• Infrared conformality and bulk critical points: SU(2) with heavy adjoint quarks
• QCD in magnetic field, Landau levels and double-life of unbroken center-symmetry
• Multiple breaking patterns in the Brout-Englert-Higgs effect beyond perturbation theory
• (Dimensional) twisted reduction in large N gauge theories
• A comparison of updating algorithms for large N reduced models
• Large $N$ reduction in deformed Yang-Mills theories
• Integrating out lattice gauge fields