Nonlocal lattice fermionic models on a two-dimensional torus

Abelian fermionic models described by the SLAC action on a two-dimensional finite lattice are considered. In vector U(1) models modified by introducing additional Pauli–Villars regularization, nonlocal effects are suppressed, and the results are in good agreement with the continuous-theory results. For chiral fermions, the lattice determinant phase differs from the determinant phase in the continuous theory.