230 research outputs found
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 , for space-time dimension . 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
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