We have calculated the x-T phase diagram of the ${\mathrm{CuO}}_{\mathit{x}}$ planes assuming screened-Coulomb repulsions between O ions up to the fifth-nearest neighbors. The repulsion between second-nearest neighbors with a Cu in between is reduced by charge-transfer effects. We used the 3×3-point approximation of the cluster-variation method. We show that this approximation fails for low temperature (T) and 1/3<x<1/2. The region of failure enlarges for smaller basic clusters. Except inside this zone or at very low T, all phase boundaries are continuous. Except at very high T, the tetragonal phase is short-range ordered.

• Received 23 April 1991

DOI:https://doi.org/10.1103/PhysRevB.44.7102