Phase diagram of a two-dimensional lattice-gas model of oxygen ordering in YBa₂Cu₃O_z with realistic interactions

We have determined a first-principles temperature-composition phase diagram describing the ordering of oxygen atoms in the ‘‘chain’’ layers of YBa₂Cu₃O_z. The calculations are based on a transfer-matrix finite-size-scaling study of a two-dimensional lattice-gas Hamiltonian (the asymmetric next-nearest-neighbor Ising [ASYNNNI] model). The interaction parameters are obtained from ab initio electronic structure calculations. The resulting phase diagram compares favorably with experiment. We analyze its sensitivity to the relative size of the interactions. We also show that the addition of a third-neighbor interaction has a minimal effect on the phase boundaries. Based on these results, we assess the applicability of the ASYNNNI model to YBa₂Cu₃O_z.