Renormalization Group Therapy

TL;DR

This paper identifies a problem with standard methods for deriving effective actions from decimated lattice configurations in MCRG, and proposes a fine-tuned approach to obtain actions that accurately reproduce the original physics.

Contribution

It highlights a common issue in MCRG decimation procedures and introduces a refined single-plaquette improved action that avoids this problem.

Findings

Standard decimation methods can produce inaccurate effective actions.

Fine-tuning decimation procedures improves the accuracy of the effective action.

A specific improved action with five group representations is proposed.

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.