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A mean field theory of the s-component Potts spin glass model is presented and is shown to reduce to TAP theory for s=2 (Ising). The paramagnetic free energy has instabilities for temperatures which agree with those derived using replica theory. The ordered phases, however, indicate that the transition is first order for s>2, in apparent contradiction with what has been obtained with replica theory.
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Lage et al. (1984) studied this question.
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