  Simulations of pure-gauge SU(2) lattice gauge theory are performed in the
minimal Coulomb gauge. This leaves a residual or remnant gauge symmetry still
active which is global in three directions but still local in one. Using
averaged fourth-dimension pointing links as a spin-like order parameter, the
remnant symmetry appears to undergo spontaneous symmetry breaking at around
$\beta = 2.6$. Both the Binder cumulant and the magnetization itself exhibit
crossings in this region using lattices up to $20^4$, and a susceptibility peak
is also observed. Finite size scaling indicates a weak first-order transition.
The symmetry breaking is also observed to take place in the fundamental-adjoint
plane, and is coincident with the strong first-order transition that exists
there at large $\beta_{\rm{adjoint}}$. This provides confirmation that this
phase transition is a symmetry-breaking transition. A well-known theorem
concerning the instantaneous Coulomb potential has previously proven that a
transition where such a Coulomb-gauge remnant symmetry breaks is necessarily
deconfining.
