  Lattice gauge theories are considered with a partial axial gauge fixing along
one direction only. This leaves a residual gauge symmetry that is still local
in three directions but now global in one. It is found that this $N^{d-1}$ fold
symmetry (on an $N^d$ lattice) breaks spontaneously at weak coupling with the
gauge field elements on links averaged over 1-d chains along the gauge-fixing
direction as order parameters. This phase transition is observed with
Monte-Carlo simulations for both 3-d Z2 and 4-d SU(2) pure gauge theories and
appears to be coincident with the deconfinement transition. This work calls
into question the equivalence of different gauges in certain circumstances.
