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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.
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Goldbart et al. (1986) studied this question.
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