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

TL;DR

This paper presents a counterexample showing that the ratio of shear viscosity to entropy density (eta/s) does not universally reach a minimum at phase transitions, challenging previous assumptions about its behavior.

Contribution

The authors provide a counterexample with two weakly interacting scalar fields demonstrating eta/s decreases monotonically, contradicting the presumed universal minimum at phase transitions.

Findings

eta/s does not always reach a minimum at phase transition

Counterexample involves two non-interacting scalar fields

eta/s decreases monotonically despite phase transition

Abstract

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.