  We study the confinement-deconfinement transition in $SU(2)$ gauge theory in
the presence of massless bosons using lattice Monte Carlo simulations. The
nature of this transition depends on the temporal extent ($N_\tau$) of the
Euclidean lattice. We find that the transition is a cross-over for $N_\tau=2,4$
and second order with $3D$ Ising universality class for $N_\tau=8$. Our results
show that the second order transition is accompanied by realization of the
$Z_2$ symmetry.
