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It is proposed to understand finite dimensional spin glasses using a 1/m expansion, where m is the number of spin components. It is shown that this approach predicts a replica symmetric state in finite dimensions. The point about which the expansion is made, the infinite-m limit, has been studied in the mean-field limit in detail and has a very unusual phase transition, rather similar to a Bose-Einstein phase transition but with N(2/5) macroscopically occupied low-lying states.
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Aspelmeier et al. (2004) studied this question.
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