Thermodynamic potential of the Polyakov loop in SU(3) quenched lattice QCD

Using SU(3) lattice quantum chromodynamics (QCD), we study for the first time the effective potential of the Polyakov loop [Formula: see text] at finite temperature, i.e. the thermodynamic potential, in the field-theoretical way. In the framework of the reweighting method in lattice QCD, we express the effective potential [Formula: see text] using the expectation value without a source term. In particular, we consider the most difficult and interesting case of vacuum coexistence at the critical temperature [Formula: see text]. We adopt SU(3) quenched lattice QCD on [Formula: see text] at [Formula: see text], which corresponds exactly to the critical temperature [Formula: see text] of the deconfinement phase transition, and use 200,000 Monte Carlo configurations. After categorizing the gauge configurations into one [Formula: see text]-symmetric and three [Formula: see text]-broken vacua each, we perform a vacuum-associated reweighting method, using the gauge configurations around each vacuum separately. Finally, we obtain the Polyakov-loop effective potential, which is well depicted around the [Formula: see text]-symmetric and [Formula: see text]-broken vacua.