Minimum of eta/s and the phase transition of the linear sigma model in the large-N limit

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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 controlled 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.
© 2009 The American Physical Society. The authors thank A. Gómez Nicola, D. Fernández Fraile, F. Sols, and D. Antonov for useful discussions as well as T. Schaefer and N. Demir for providing us their=s data. This work was supported by Grants No. FPA2007-29115-E, No. PR34-1856-BSCH, No. FPA2008-00592, No. FIS2008-01323, No. UCM-BSCH GR58/08 910309, UCM-Santander No. PR34/07-15875, and an FPU grant to J. M. T.-R.
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