  Monte Carlo simulations are performed on the three-dimensional (3D) Ising
model with the 2-1-4 layered perovskite structure as a minimal model for
checkerboard charge ordering phenomena in layered perovskite oxides. Due to the
interlayer frustration, only 2D long-range order emerges with a finite
correlation length along the c axis. Critical exponents of the transition
change continuously as a function of the interlayer coupling constant. The
interlayer long-range Coulomb interaction decays exponentially and is
negligible even between the second-neighbor layers. Instead, monoclinic
distortion of a tetragonal unit cell lifts the macroscopic degeneracy to induce
a 3D charge ordering. The dimensionality of the charge order in
La$_{0.5}$Sr$_{1.5}$MnO$_4$ is discussed from this viewpoint.
