Thermodynamic Potential of the Polyakov Loop in SU(3) Quenched Lattice QCD

Using SU(3) lattice QCD, we study the effective potential of the Polyakov loop P at finite temperature, i.e., the thermodynamic potential, in the field-theoretical manner for the first time. In the framework of the reweighting method in lattice QCD, we express the effective potential Veff( P ) using the expectation value with no source term. In particular, we deal with the most difficult and interesting case of vacuum coexistence at the critical temperature Tc. We adopt SU(3) quenched lattice QCD on 48³ × 6 at β= 5.89379, just corresponding to the critical temperature Tc of the deconfinement phase transition, and use 200,000 Monte Carlo configurations. After categorizing the gauge configurations into each of Z₃-symmetric and three Z₃-broken vacua, we perform a vacuum-associated reweighting method where gauge configurations around each vacuum are separately used. We eventually obtain the Polyakov-loop effective potential, which is well depicted around the Z₃-symmetric and Z₃-broken vacua.