The Study Of Phase Transition Of Thermal QED₃ At Finite Volume

Quantum electrodynamics in 2+1 dimensions（QED₃）has been studied as a theoretical laboratory for many years.Due to its similarities to quantum chromodynamics（QCD）such as dynamical chiral symmetry breaking（DCSB）and confinement,QED₃is considered to be a simple analogy that has a great significance in understanding fundamental characteristics of QCD,which is hard to investigate because of its non-Abelian nature.Over the past few decades,the chiral phase transition（CPT）of QED₃has been extensively studied.People found that CPT happens when the number of flavors of fermions reaches a critical value,which is about 3.5 zt zero temperature.At finite temperature,people solved the DS equation of fermions based on the imaginary-time thermal field theory formula and found that there is a critical temperature T_c,beyond which the chiral symmetry gets restored.Later on,researchers took more impact factors of chiral phase transition into account and studied different kinds of properties of the QED₃at finite temperature as well as density,and they made further investigation of the phase structure of QED₃.This thesis is aimed at utilizing the DS equation（DSE）to study chiral phase transition of QED₃at finite temperature and volume.DS equation provides a non-perturbative approach to quantum field theory,under the framework of DSE,we analyze the phase structure of QED₃in the rainbow approximation.According to Landau theory of continuous phase transition,we adopt the CJT effective potential and calculate its first and second derivative,which refer to entropy and specific heat respectively.Here is the majority of our works:In the chiral limit,we choose chiral condensate as the order parameter,and obtain its value in the cases of system volume L=200,300,400.With the increasing of temperature,the chiral condensate diminishes and vanishes at a critical temperature T_c,over the critical temperature,the system switch from chiral symmetry breaking phase to chiral symmetric phase.The entropy increases continuously in the symmetric phase but manifests a kink at T_cwhere CPT happens,it shows a slope reduction over the critical temperature.The value of specific heat in the chiral symmetric phase and chiral symmetry broken phase are continuous separately,but manifest a jumping near to the critical temperature,which exhibits a signal for second-order phase transition.Moreover,the critical temperature reduces with the decreasing of system volume.Beyond the chiral limit,fermion obtains a small nonzero mass,we choose different mass of fermion in the finite volume systems and find that the descent rate of chiral condensate becomes smaller with the increasing mass of fermion.Most previous studies show that massive fermion system is spontaneous chiral symmetry broken all the time,and the system undergoes a crossover.In this study,we found a critical vale of fermion mass m_cwhich decreases with the increasing of system volume.For a massive fermion system with its mass below m_c,the chiral symmetry can get restored and the system undergoes a second-order phase transition,while for the system with its mass beyond critical mass,the chiral symmetry cannot get restored and CPT is still a crossover.