A Research On The Phase Transition Of Strong Interaction Matter

Quantum chromodynamics(QCD)is a theory that describes strong interactions.It has two non-perturbative features,which are Dynamical Chiral Symmetry Breaking and color confinement.The former describes the mass origin of hadrons,while the latter describes the phenomenon that free quarks with color is isolated.Under extreme condi-tions,for example high temperature,high density and strong external magnetic fields,the strong-interaction matter may undergo chiral phase transition and deconfinement phase transition.Therefore,strong-interaction matter has rich phase structures.In this thesis,we first investigate the nuclear symmetry energy.Starting from the model-independent Lagrangian,the model-independent nuclear symmetry energy for-mula is obtained by using the functional path integral approach.It is found that the nuclear symmetry energy is determined by the product of the nucleon number density and the reciprocal of the isospin susceptibility,the latter can be used as a probe for the chiral phase transition at finite density.The model-independent nuclear symmetry energy formula can be regarded as a bridge,which links nuclear physics to particle physics.In principle,if the well known Fermion sign problem is solved,nuclear sym-metry energy can be directly given by the lattice QCD simulation from the quark-gluon degree of freedom,regardless of the detailed process of the hadronization.Since the principle of quark-hadron duality,we calculated the isospin susceptibility by using the Nambu-Jona-Lasinio(NJL)model.It is found that the isospin susceptibility shows a mutation at critical chemical potential of the chiral phase transition,thus the corre-sponding nuclear symmetry also shows an abrupt change at the corresponding critical density.Then,the deconfinement phase transition of three dimensional quantum electro-dynamics(QED3)is investigated.Analogy to the case of QCD,in which the dual quark condensate is regarded as an order parameter of deconfinmement phase transition,the relationship between fermion dual condensate and Z symmetry in QED3 is set up.The latter is considered to be related to deconfinement phase transition in QED3.Therefore,the fermion dual condensate can also be regarded as an order parameter of deconfin-mement phase transition in QED3.By using the framework of the Dyson-Schwinger equations,we find that the deconfinement phase transition in QED3 is a crossover.As increase of fermion mass,the pseudo-critical temperature of deconfinement crossover also increases.Different from QCD,the pseudo-critical temperature is smaller than the pseudo-critical temperature of the chiral phase transition.At last,we study the strong interaction matter phase transition in an external mag-netic field.The fermion propagator in an external constant magnetic field is given and the approach,which is different from Schwinger proper time method,is used.Then the NJL model is adopted to perform calculation.It is found that the dynamical quark mass increases with the strength of external magnetic field,which is magnetic catalysis.We also study the critical behavior of phase transitions.In the chiral limit,the QCD phase transition is a second phase transition at finite temperature.We calculate different criti-cal exponents of chiral phase transition in the chiral limit.It is found that under a strong magnetic field,all the four critical exponents show a slight change.