Finite-size effects on a lattice calculation

We study in this paper the finite-size effects of a non-periodic lattice on a lattice calculation. To this end we use a finite lattice equipped with a central difference derivative with homogeneous boundary conditions to calculate the bosonic mass associated to the Schwinger model. We found that the homogeneous boundary conditions produce absence of fermion doubling and chiral invariance, but we also found that in the continuum limit this lattice model does not yield the correct value of the boson mass as other models do. We discuss the reasons for this and, as a result, the matrix which cause the fermion doubling problem is identified.