Interplay between mass, volume, vacuum angle, and chiral condensate in N-flavor two-dimensional QED

The Schwinger model (QED(2)) with N flavors of massive fermions on a circle of circumference L, or equivalently at finite temperature T, is reduced to a quantum-mechanical system of N-1 degrees of freedom. With degenerate fermion masses (m) the chiral condensate develops a cusp singularity at theta=+/-pi in the limit L-->infinity or T-->0, which is removed by a large asymmetry in the fermion masses. Physical quantities sensitively depend on the parameter mL, or m/T, and the m-->0 and L-->infinity (or T-->0) limits do not commute. A detailed analysis is given for N=3.