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

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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 β= 4/g² = 1.96± 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 ν= 0.99 ± 0.13. The existence of this transition suggests a second transition from spin glass to ferromagnet should exist at higher β.