<physics>Think of it as a condensed-matter phase transition between a weakly-coupled regime and a strongly-coupled regime (or one with long-range correlations - probably strongly coupled via duality). Linear (mean-field) techniques to describe the environment of a single component of the sytem are appropriate when the back-reaction of a single element on the hole system is negligible. But in the strongly-coupled/long-range-correlated regime different kinds of techniques are needed even to describe the local environment, because of backreaction.</physics>

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