Anomalous behavior in the massive Schwinger model

We evaluate the chiral condensate and Polyakov loop in two-dimensional QED with a fermion of an arbitrary mass (m). We find a discontinuous m dependence in the chiral condensate and an anomalous temperature dependence in Polyakov loops when the vacuum angle π ∼ π and m = O(e). These nonperturbative phenomena are due to the bifurcation process in the solutions to the vacuum eigenvalue equation.