CJT effective potential approach to analyze the nature of phase transition of thermal QED $$_3$$ 3 at finite volume

Abstract

Abstract Based on the Cornwall–Jackiw–Tomboulis effective potential and the truncated Dyson–Schwinger equations, the nature of phase transition of thermal QED $$_3$$ 3 at finite volume is investigated. We show that, with the rise of temperature, the system undergoes a second-order transition in the chiral limit, and remains exhibiting the second-order with small fermion mass, while it switches to a crossover when the fermion mass exceeds a critical value about $$m_{c}$$ m c , which diminishes with the increasing volume size and tends to zero in infinite volume.