Minimum of $\eta/s$ and the phase transition of the Linear Sigma Model in the large-N limit

TL;DR

This paper investigates whether the minimum of the shear viscosity to entropy density ratio (eta/s) can serve as an indicator of phase transitions, using the Linear Sigma Model at large-N as a controlled theoretical framework.

Contribution

It provides a detailed analysis confirming that eta/s reaches a minimum near the second order phase transition in the Linear Sigma Model at large-N, supporting its use as a diagnostic tool.

Findings

eta/s minimum occurs near the second order phase transition

The minimum is associated with rapid changes in the order parameter

The study confirms eta/s as a potential indicator of phase transitions

Abstract

We reexamine the possibility of employing the viscosity over entropy density ratio as a diagnostic tool to identify a phase transition in hadron physics to the strongly coupled quark-gluon plasma and other circumstances where direct measurement of the order parameter or the free energy may be difficult. It has been conjectured that the minimum of eta/s does indeed occur at the phase transition. We now make a careful assessment in a controled theoretical framework, the Linear Sigma Model at large-N, and indeed find that the minimum of eta/s occurs near the second order phase transition of the model due to the rapid variation of the order parameter (here the sigma vacuum expectation value) at a temperature slightly smaller than the critical one.