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 the Monte Carlo renormalization group, i.e., that the decimated configurations are equilibrium configurations of the adopted form of the effective action, can be achieved only by careful fine-tuning of the choice of decimation prescription and/or action.

Figure 1

Demon fundamental representation energy flow for DSB decimation and action (1) at various $c$ values.

Figure 2

Demon $1\times 1$ and $1\times 2$ loop energy flow for DSB decimation at $c=0.161$.

Figure 3

Demon $1\times 1$ loop energy flow for Swendsen decimation at various $c$ values.

Figure 4

Demon $1\times 2$ loop energy flow for Swendsen decimation at various $c$ values.

Figure 5

$W_{N\times N}^{\mathrm{dec}}$ and $W_{N\times N}^{\mathrm{gen}}$ plotted for each decimation type. From Table .