Nature of chiral phase transition in QED$_3$ at zero density

Based on the feature of chiral susceptibility and thermal susceptibility at finite temperature, the nature of chiral phase transition around the critical number of fermion flavors ($N_c$) and the critical temperature ($T_c$) at a fixed fermion flavors number in massless QED$_3$ are investigated. It is showed that, at finite temperature the system exhibits a second-order phase transition at $N_c$ or $T_c$ and each of the estimated critical exponents is less than 1, while it reveals a higher-order continuous phase transition around $N_c$ at zero temperature.