Gauge-invariant spin glasses

Spin-glass models with orthogonal and unitary bond interactions are investigated using replica mean-field theory. The orthogonal model leads to a low-temperature phase described by a Parisi replica symmetry broken order parameter. The analogous solution for the unitary model is unstable to fluctuations which render the order parameter complex. In this case a simple parametrization of the Hermitian order parameter suggests a first-order transition.