We derive and compare various forms of local semicircle laws for random matrices with exchangeable entries which exhibit correlations that decay at a very slow rate. In fact, any $l$-point correlation will decay at a rate of $N^{-l/2}$. We call our ensembles \emph{of Curie-Weiss type}, and Curie-Weiss($β$)-distributed entries are admissible as long as $β\leq 1$.
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