  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.
