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## Renormalization group and universality

I think you're overestimating the universality concept. There are many "classes of universality", and many new of them appear every year in the scientific literature.

Imagine that you have a microscopic model, characterized by a series of "operators" $O_i$. When you renormalize (i.e.: see things from far away, you blur the details) some of them increase their importance and some of them decrease. The first are called relevant, and the second irrelevant. There are even "marginal" operators, which neither increase or decrease. Fixed points of the renormalization group, or universality classes, are characterized by the set of relevant operators. It's not like you have a single all-encompassing universality class. No, it depends on the operators, so it depends on your theory.