Renormalization group therapy

We point out a general problem with the procedures commonly used to obtain improved actions from Monte Carlo Renormalization Group (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) lattice gauge theory using Swendsen and '' double smeared blocking '' decimation procedures. A single-plaquette improved action involving five group representations and nearly free of this pathology is given.