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For second order phase transition thermodynamic properties can be described in very general terms by their critical exponents. So at every transition the correlation length $\xi$ should diverge as $$\xi \propto |T-Tc|^{-\nu},$$ where the exponent depends on the specifics of the system. Is the same true for the correlation time $\tau$ or only in special cases? Additionally if the correlation time diverges how can there still be fluctuations, isn't everything infinitely strongly coupled together as $\tau \rightarrow \infty$?

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