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Fixed point action for the massless lattice Schwinger model

We determine non-perturbatively the fixed-point action for fermions in the two-dimensional U(1) gauge (Schwinger) model. This is done by iterating a block spin transformation in the background of non-compact gauge field configurations sampled according to the (perfect) Gaussian measure. The resulting action has 123 independent couplings, is bilinear in the Grassmann fields, gauge-invariant by considered the compact gauge transporters and localized within a $7\times 7$ lattice centered around one of the fermions. We then simulate the model at various values of $β$ and compare with results obtained with the Wilson fermion action. We find excellent improvement for the studied observables (propagators and masses).