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In statistical mechanics renormalization is often related to coarse-graining which in turn allows to calculate some macroscopic states. The resulting macroscopic description is sometimes called emergent. However, in general, the emergent properties do not always result from the granularity of description. For example, critical behavior and long-range correlations are not supposed to be affected by coarse-graining. Without going into mathematical details, I am trying to get an intuition that connects renormalization and emergence in general. What are the types of emergence that can not be described via renormalization? Is quantum decoherence one of them?

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