Effective lattice theories for Polyakov loops

Abstract

We derive effective actions for SU(2) Polyakov loops using inverse Monte Carlo techniques. In a first approach, we determine the effective couplings by requiring that the effective ensemble reproduces the single-site distribution of the Polyakov loops. The latter is flat below the critical temperature implying that the (untraced) Polyakov loop is distributed uniformly over its target space, the SU(2) group manifold. This allows for an analytic determination of the Binder cumulant and the distribution of the mean-field, which turns out to be approximately Gaussian. In a second approach, we employ novel lattice Schwinger-Dyson equations which reflect the SU(2) x SU(2) invariance of the functional Haar measure. Expanding the effective action in terms of SU(2) group characters makes the numerics sufficiently stable so that we are able to extract a total number of 14 couplings. The resulting action is short-ranged and reproduces the Yang-Mills correlators very well.

arXiv comment27 pages, 8 figures, v2: method refined, chapter and references added

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• Two-colour QCD with heavy quarks at finite densities
• Inverse Monte-Carlo determination of effective lattice models for SU(3) Yang-Mills theory at finite temperature
• Phase Structure of Z(3)-Polyakov-Loop Models
• Effective Actions for the SU(2) Confinement-Deconfinement Phase Transition
• Zero Point Energy of Renormalized Wilson Loops
• Effective Polyakov line action from the relative weights method
• Finding the effective Polyakov line action for SU(3) gauge theories at finite chemical potential
• Eigenvalue repulsion in an effective theory of SU(2) Wilson lines in three dimensions
• Effective Polyakov line action from strong lattice couplings to the deconfinement transition
• Free energy for parameterized Polyakov loops in SU(2) and SU(3) lattice gauge theory
• Effective Polyakov Loop Dynamics for Finite Temperature G(2) Gluodynamics
• Equilibrium criterion and effective spin models for finite temperature gauge theories
• Ward Identities for Invariant Group Integrals
• Effective potential for Polyakov loops from a center symmetric effective theory in three dimensions
• Generalized Potts-Models and their Relevance for Gauge Theories
• $\xi /{\xi }_{2nd}$ ratio as a tool to refine Effective Polyakov Loop models
• Lattice simulation of a center symmetric three-dimensional effective theory for SU(2) Yang-Mills
• The $\xi /{\xi }_{2nd}$ ratio as a test for Effective Polyakov Loop Actions
• Effective Lattice Actions for Finite-Temperature Yang-Mills Theory