The interplay between mass, volume, θ, and <ψ> in N-flavor QED₂

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The Schwinger model (QED₂) 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 θ=± π in the limit L -> ∞ 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 -> ∞ (or T -> 0) limits do not commute. A detailed analysis is given for N=3.