Chiral Phase Transition And ? Condensation With Magnetic Field In The PNJL Model

Quantum Chromodynamics(QCD)is widely believed to be the theory of the strong interactions.Investigations on its rich vacuum structure and how the QCD vacuum can be modified in extreme environment are among the major theoretical challenges in modern physics.It is in particular an interesting topic to study how non-perturbative features of QCD are affected by thermal excitations at high temperature T and by baryon-rich constituents at large quark chemical potential?g.Such research on hot and dense QCD is important not only from the theoretical point of view but also for numerous applications to the physics problems of the Quark-Gluon Plasma,ultra-dense and cold nuclear matter as could exist in the interior of compact stellar objects,and so on.The most intriguing non-perturbative aspects of the QCD vacuum at low energy are color confinement and spontaneous breakdown of chiral symmetry.In recent years our knowledge on the QCD phase diagram has increased noticeably.In addition to hot and dense QCD with T and ?q,the effect of a strong magnetic field on the QCD vac-uum structure is also a very hot subject.This paper is major on the chiral condensation,the ? condensation,the trace of polyakov loop of two flavour quark matter change with temperature and isospin chemical potential with magnetic field in the PNJL model.At the beginning of the this paper we use the initial lagrangian to drive,after the trace of Dirac space,flavour space and color space.Finally we get the explict expression of the thermodynamic potential.We have to take the derivative of chiral condensation,the 7r condensation and the trace of polyakov loop through thermodynamic potential.So we get four cou-pling equation.In the farmwork the hadron chemical potential value is zero,we dealed with the math results which how chiral conden,sation,the ? condensation,the trace of polyakov loop are affected by magnetic field or not.We contrast phase structure of two kinds cases,we find when with magnetic field in the farmework,the chiral conden-sation,the ? condensation,the trace of polyakov loop have apparent change contrasted without magnetic field.Chiral condensation will be oscilate,the ? condensation will become larger with the increase of the magnetic field,while the trace of polyakov loop,decreases with the increase of the magnetic field.