Phase diagram and low-temperature behavior of oxygen ordering in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{\mathit{z}}$ using ab initio interactions

The phase diagram and oxygen ordering in ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{\mathit{z}}$ are investigated, on a first-principles basis, by means of an asymmetric next-nearest-neighbor Ising model using Monte Carlo and cluster-variation-method statistics. It is shown that saturation of some pair-correlation functions at low temperature to a concentration-independent value makes the model quasi-one-dimensional. This correspondence between the two- and one-dimensional model explains some typical characteristics of the phase diagram at low temperature and provides a simple argument for the existence of a low-temperature, low-O-concentration, orthorhombic phase.