Improving the improved action

TL;DR

This paper explores how to properly construct improved actions in SU(2) gauge theory using Monte Carlo Renormalization Group methods, emphasizing the importance of fine-tuning decimation procedures for accurate results.

Contribution

It demonstrates that achieving self-consistency in MCRG requires careful fine-tuning of decimation procedures and effective actions in SU(2) gauge theory.

Findings

Proper fine-tuning is essential for self-consistency in MCRG.

Different decimation procedures impact the equilibrium configurations.

Effective actions must be carefully chosen to match decimated configurations.

Abstract

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.