Phase diagram and surface tension in the three-flavor Polyakov-quark-meson model

TL;DR

This paper develops a real-valued effective potential for the three-flavor Polyakov-Quark-Meson model, enabling detailed phase diagram analysis, surface tension calculations, and insights into phenomena like the fermion sign problem.

Contribution

It introduces a method to obtain a real effective potential in the three-flavor model, facilitating the study of phase transitions and surface tension in a unified framework.

Findings

Phase diagram and equilibrium observables computed in mean-field approximation.

Surface tension between phases calculated, matching two-flavor model results.

Explicit demonstration of the fermion sign problem in the model.

Abstract

We obtain the in-medium effective potential of the three-flavor Polyakov-Quark-Meson model as a real function of real variables in the Polyakov loop variable, to allow for the study of all possible minima of the model. At finite quark chemical potential, the real and imaginary parts of the effective potential, in terms of the Polyakov loop variables, are made apparent, showing explicitly the fermion sign problem of the theory. The phase diagram and other equilibrium observables, obtained from the real part of the effective potential, are calculated in the mean-field approximation. The obtained results are compared to those found with the so-called saddle-point approach. Our procedure also allows the calculation of the surface tension between the chirally broken and confined phase, and the chirally restored and deconfined phase. The values of surface tension we find for low temperatures are very close to the ones recently found for two-flavor chiral models. Some consequences of our results for the early Universe, for heavy-ion collisions, and for proto-neutron stars are briefly discussed.