The Quantum and Local Polyakov loop in Chiral Quark Models at Finite   Temperature
  We describe results for the confinement-deconfinement phase transition as predicted by the Nambu--Jona-Lasinio model where the local and quantum Polyakov loop is coupled to the constituent quarks in a minimal way (PNJL). We observe that the leading correlation of two Polyakov loops describes the chiral transition accurately. The effects of the current quark mass on the transition are also analysed. 
E. Megias, E. Ruiz Arriola and L.L. Salcedo