Unlike ferromagnetic spin models, a spin glass has a highly non-trivial phase transition profile. For mean field models (the SK spin glass), the glass experiences a replica-symmetry breaking phenomenon that is only fully understood recently. However, for short-range models, almost nothing is known rigorously, including basic problems such as the nature of the glass transition. A potential route towards settling such problems may rely on a suitable generalization of the random cluster model as a universal statistical tool.
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