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SU(2) lattice gauge theory is extended to a larger coupling space where thecoupling parameter for horizontal (spacelike) plaquettes, $\beta_H$, differsfrom that for vertical (Euclidean timelike) plaquettes, $\beta_V$. When$\beta_H \rightarrow \infty$ the system, when in Coulomb Gauge, splits intomultiple independent 3-d O(4) Heisenberg models on spacelike hyperlayers.Through consideration of the robustness of the Heisenberg model phasetransition 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 toanother edge due to its symmetry-breaking nature, and therefore mustnecessarily cross the $\beta_V = \beta_H$ line at a finite value. Indeed, ahigher-order SU(2) phase transition is found at $\beta = 3.18 \pm 0.08$, from afinite-size scaling analysis of the Coulomb gauge magnetization from MonteCarlo simulations, which also yields critical exponents. An important technicalbreakthrough is the use of open boundary conditions, which is shown to reducesystematic and random errors of the overrelaxation gauge-fixing algorithm by afactor of several hundred. The string tension and specific heat are also shownto be consistent with finite-order scaling about this critical point using thesame critical exponents.

Connecting phase transitions between the 3-d O(4) Heisenberg model and 4-d SU(2) lattice gauge theory