  We present lattice simulations of a center symmetric dimensionally reduced
effective field theory for SU(2) Yang Mills which employ thermal Wilson lines
and three-dimensional magnetic fields as fundamental degrees of freedom. The
action is composed of a gauge invariant kinetic term, spatial gauge fields and
a potential for the Wilson line which includes a "fuzzy" bag term to generate
non-perturbative fluctuations. The effective potential for the Polyakov loop is
extracted from the simulations including all modes of the loop as well as for
cooled configuration where the hard modes have been averaged out. The former is
found to exhibit a non-analytic contribution while the latter can be described
by a mean-field like ansatz with quadratic and quartic terms, plus a
Vandermonde potential which depends upon the location within the phase diagram.
