Renormalization Group Therapy

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.Comment: 18 pages, 9 figures, 9 table

Improving the improved action

We investigate the construction of improved actions by the Monte Carlo Renormalization Group method in the context of SU(2) gauge theory utilizing different decimation procedures and effective actions. We demonstrate that the basic self-consistency requirement for correct application of MCRG, i.e. that the decimated configurations are equilibrium configurations of the adopted form of the effective action, can only be achieved by careful fine-tuning of the choice of decimation prescription and/or action.Comment: 8 pages, 5 figure

Deriving confinement via RG decimations

We present the general framework and building blocks of a recent derivation of the fact that the SU(2) LGT is in a confining phase for all values of the coupling $0 < \beta < \infty$, for space-time dimension $d \leq 4$. The method employs approximate but explicitly computable RG decimations that are shown to constrain the exact partition function and order parameters from above and below, and flow from the weak to the strong coupling regime without encountering a fixed point.Comment: 7 pages, presented at the XXV International Symposium on Lattice Field Theoy, July 30 - August 4 2007, Regensburg, German