  A new order parameter is constructed for SU(2) lattice gauge theory in the
context of the two-real-replica method normally used for spin glasses. The
order parameter is sensitive to a global Z2 subgroup of the gauge symmetry
which is seen to break spontaneously at $\beta = 4/g^2 = 1.96\pm 0.01$. No
gauge fixing is required. Finite size scaling is consistent with a high-order
paramagnet to spin glass transition with a critical exponent $\nu = 0.99 \pm
0.13$. The existence of this transition suggests a second transition from spin
glass to ferromagnet should exist at higher $\beta$.
