Aspects Of QCD Chiral Phase Transition

Strong interaction is one of the four fundamental interactions known to human be-ings.As a gauge field theory with local SU(3)symmetry,Quantum Chromodynamics describes the strong interaction among quarks and gluons.The unique characters of QCD like asymptotic freedom etc.creat a rich connotation in physics as well as present var-ious phase structures.Understanding QCD phase diagram is important in many fields in physics,such as the evolution of the early universe,heavy-ion collisions,structure of compact stars.People use heavy ion colliders to produce matter at high temperature and density,i.e.quark-gluon plasma,in order to study the phase structure and properties of matter under extreme conditions.It is widely believed that a crossover exists at the small chemical potential region on the QCD phase diagram.The investigation of the critical endpoint becomes very important in QCD studies.Howerver,due to the non-perturbative nature of QCD theory,it is impossible to perform analytical calculations directly from QCD.People developed a large number of effective theories through which the phase properties of QCD could be qualtively probed.We use an renormalizable effective theory of QCD with spontaneous breaking and restoration of chiral symmetry to model the QCD matter under finite chemical potential and temperature.We use thermodynamic geometry to investigate the QCD phase diagram.We find that the thermodynamic curvature R changes its sign around the crossover and its magnitude diverges when approaching the critical endpoint,which supports the idea that R ? ?d.We investigate further and analyze the reason for the divergent behavoir of the thermodynamic curvature and found the mixed susceptibility of energy and baryon number fluctuation might play an important role in the divergent behavior of R,leading to the critical phenomenon.Moreover,we also study the chrial phase transition in a finite-size system.A very interesting discovery is that,at small temperatures,if the system is small enough,the zero-mode plays an important role in the chiral phase transition.In a system of 3fm,the zero-mode excitation creats a intermediate transition,but unable to restore the broken chiral symmetry.In smaller systems,the effect of the zero-mode enhances as to directly restore the chiral symmetry.When the system is large,the effect of the zero-mode will be overwhelmed by the increasing number of higher excitations.The zero-mode effect appears only in a finite-size system.