Renormalization Group Therapy

Abstract

We point out a general problem with the procedures commonly used to obtain improved actions from MCRG decimated configurations. Straightforward measurement of the couplings from the decimated configurations, by one of the known methods, can result into actions that do not correctly reproduce the physics on the undecimated lattice. This is because the decimated configurations are generally not representative of the equilibrium configurations of the assumed form of the effective action at the measured couplings. Curing this involves fine-tuning of the chosen MCRG decimation procedure, which is also dependent on the form assumed for the effective action. We illustrate this in decimation studies of the SU(2) LGT using Swendsen and Double Smeared Blocking decimation procedures. A single-plaquette improved action involving five group representations and free of this pathology is given.

18 pages, 9 figures, 9 tables

References in corpus (10)

• Quark confinement and the bosonic string
• Locality and exponential error reduction in numerical lattice gauge theory
• Prospects for perfect actions
• Renormalization group flow of SU(3) lattice gauge theory - Numerical studies in a two coupling space
• SU(3) lattice gauge theory with a mixed fundamental and adjoint plaquette action: Lattice artefacts
• Canonical Demon Monte Carlo Renormalization Group
• Biased Metropolis-Heat-Bath Algorithm for Fundamental-Adjoint SU(2) Lattice Gauge Theory
• Towards a perfect fixed point action for SU(3) gauge theory
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Cited by in corpus (8)

• Infrared fixed point of the 12-fermion SU(3) gauge model based on 2-lattice MCRG matching
• Inverse Monte-Carlo determination of effective lattice models for SU(3) Yang-Mills theory at finite temperature
• Series expansions of the density of states in SU(2) lattice gauge theory
• Equilibrium criterion and effective spin models for finite temperature gauge theories
• Improving the improved action
• String tension and removal of lattice coarsening effects in Monte Carlo Renormalization Group
• Improved actions and lattice coarsening effects in MCRG studies in SU(2) LGT
• Critical couplings and string tensions via lattice matching of RG decimations