6 págs.; 7 figs.; PACS number s : 71.10.Fd, 71.10.Hf, 71.30. h We show in this paper that the single-particle spectral-weight function (SWF) of the one-dimensional ionic Hubbard model at half filling exhibits critical behavior, as a function of the on-site repulsion U, near the chemical potential. The calculation has been carried out within the framework of the cluster perturbation theory approach of Senechal, Phys. Rev. Lett 84, 522 (2000). As U increases, the SWF at kF=±π 2 (the Fermi points) jumps from the two-peak structure (plus two weak side peaks) characteristic of low U