The Study Of Several Phase Transition Order Parameters In The Quark-meson Model

Whether dual meson condensates can indicate deconfinement are investigated in a Polyakov-loop enhanced linear sigma model by imposing the twisted boundary conditions.They are dual sigma condensate,dual pion condensate and dual vector meson condensate resoectively.It is confirmed that the rapid rise of the dual sigma condensate with T at zero density is driven by the chiral transition,no matter the Polyakov-loop dynamics and or the Dirac-sea contribution are included or not.For finite isospin chemical potential μI>mπ/2,the dual sigma condensate shows abnormal thermal behavior which decreases with T below the melting temperature TcI3,of pion superfluidity;On the other hand,even the dual pion condensate always increases with T,its maximum slope locates exactly at TcI3 rather than the deconfinement temperature TcP determined by the Polyakov-loop.The dual vector meson condensate for μI>mπ/2 is also calculated.The conclusion is this quantity is similar to Polyakov-loop when ignoring the Dirac-sea contribution,This method should be an artifact.This quantity is more sensitive to the chiral transition when taking into account the Dirac-sea contribution.Our study further suggests that it should be cautious to use the dual observables as indicators of deconfinement,at least in QCD models.