Chiral and deconfinement phase transitions in QED₃ with finite gauge boson mass

Based on the experimental observation that there is a coexisting region between the antiferromagnetic (AF) and d-wave superconducting (dSC) phases, the influences of gauge boson mass m_a on chiral symmetry restoration and deconfinement phase transitions in QED₃ are investigated simultaneously within a unified framework, i.e., Dyson–Schwinger equations. The results show that the chiral symmetry restoration phase transition in the presence of the gauge boson mass m_a is a typical second-order phase transition; the chiral symmetry restoration and deconfinement phase transitions are coincident; the critical number of fermion flavors N^c_f decreases as the gauge boson mass m_a increases, which implies that there exists a boundary that separates the N^c_f–m_a plane into chiral symmetry breaking/confinement region for (N^c_f, m_a) below the boundary and chiral symmetry restoration/deconfinement region for (N^c_f, m_a) above it.