Minimum Shear Viscosity over Entropy Density at Phase Transition? --- A Counterexample

The ratio eta/s, shear viscosity (eta) to entropy density (s), reaches its local minimum at the (second order) phase transition temperature in a wide class of systems. It was suspected that this behavior might be universal. However, a counterexample is found in a system of two weakly self-interacting real scalar fields with one of them condensing at low temperatures while the other remains in the symmetric phase. There is no interaction between the two fields. The resulting eta/s is monotonically decreasing in temperature despite the phase transition.

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