  Using a variant of the IMCRG method of Gupta and Cordery, we explicitly
compute majority rule block spin effective actions for the signs of the
Polyakov loops in 4D SU(2) finite temperature lattice gauge theories. To the
best of our knowledge, this is the first attempt to compute numerically
effective actions for the Polyakov loop degrees of freedom in 4D SU(2). The
most important observations are: 1. The renormalization group flow at the
deconfinement transition can be nicely matched with the flow of the 3D Ising
model, thus confirming the Svetitsky-Yaffe conjecture. 2. The IMCRG simulations
of the FT SU(2) model have strongly reduced critical slowing down.
