  An extended version of 4-d SU(2) lattice gauge theory is considered in which
different inverse coupling parameters are used, $\beta_H=4/g_{H}^2$ for
plaquettes which are purely spacelike, and $\beta_V$ for those which involve
the Euclidean timelike direction. It is shown that when $\beta_H = \infty$ the
partition function becomes, in the Coulomb Gauge, exactly that of a set of
non-interacting 3-d O(4) classical Heisenberg models. Long range order at low
temperatures (weak coupling) has been rigorously proven for this model. It is
shown that the correlation function demonstrating spontaneous magnetization in
the ferromagnetic phase is a continuous function of $g_H$ at $g_H =0$ and
therefore that the spontaneously broken phase enters the ($\beta_H$, $\beta_V$)
phase plane (no step discontinuity at the edge). Once the phase transition line
has entered, it can only exit at another identified edge, which requires the
SU(2) gauge theory within also to have a phase transition at finite $\beta$. A
phase exhibiting spontaneous breaking of the remnant symmetry left after
Coulomb gauge fixing, the relevant symmetry here, is non-confining. Easy
extension to the SU(N) case implies that the continuum limit of
zero-temperature 4-d SU(N) lattice gauge theories is not confining, in other
words gluons by themselves do not produce a confinement.
