Possible origin of the pseudogap end point in the high-T${}_c$ cuprates

Recent experiments find that the pseudogap phase of the high-T${}_c$ cuprates ends suddenly at an electron doping $x^{\ast }$ when the Fermi surface change its shape from hole-like to electron-like. In this short note, we argue that the antiferromagnetic(AF) spin correlation of the system should drop abruptly at the same doping. At the same time, we argue that the critical behavior observed at $x^{\ast }$ in the specific heat measurement should be attributed to the strong renormalization of the quasiparticle excitation in the anti-nodal region by the critical AF spin fluctuation. This picture also predicts that any pseudogap-like spectral feature related to AF scattering in the electron-doped cuprates should terminate at the doping level when the Fermi surface becomes tangent to the boundary of AF Brillouin zone. Recent ARPES measurement on the electron-doped cuprate Nd${}_{2-x}$Ce${}_x$CuO${}_4$ seems to be consistent with such a prediction.