  SU(2) lattice gauge theory is extended to a larger coupling space where the
coupling parameter for horizontal (spacelike) plaquettes, $\beta_H$, differs
from that for vertical (Euclidean timelike) plaquettes, $\beta_V$. When
$\beta_H \rightarrow \infty$ the system, when in Coulomb Gauge, splits into
multiple independent 3-d O(4) Heisenberg models on spacelike hyperlayers.
Through consideration of the robustness of the Heisenberg model phase
transition to small perturbations, and illustrated by Monte Carlo simulations,
it is shown that the ferromagnetic phase transition in this model persists for
$\beta_H < \infty$. Once it has entered the phase-plane it must continue to
another edge due to its symmetry-breaking nature, and therefore must
necessarily cross the $\beta_V = \beta_H$ line at a finite value. Indeed, a
higher-order SU(2) phase transition is found at $\beta = 3.18 \pm 0.08$, from a
finite-size scaling analysis of the Coulomb gauge magnetization from Monte
Carlo simulations, which also yields critical exponents. An important technical
breakthrough is the use of open boundary conditions, which is shown to reduce
systematic and random errors of the overrelaxation gauge-fixing algorithm by a
factor of several hundred. The string tension and specific heat are also shown
to be consistent with finite-order scaling about this critical point using the
same critical exponents.
