Is SU(2) lattice gauge theory a spin glass?

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 $\beta =4\mathrm{/}{g}^2=1.96\pm 0.01$. 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 $\beta$.