First-order structural phase transitions in a lattice-gas model for ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6+\mathit{x}}$

Recent experiments indicate that the structural phase transitions in the high-temperature superconductor ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{6+\mathit{x}}$ may be first order at low temperatures. The oxygen ordering in the Cu-O basal planes of this material may be described by a lattice-gas model introduced by Wille et al. B [Phys. Rev. Lett. 60, 1065 (1988)]. However, as recent numerical studies show, this model does not exhibit first-order transitions. Here, we extend the model to include weak attractive interactions (2% of the nearest-neighbor interactions) between next-nearest-neighbor oxygen chains, and we study the extended model using transfer-matrix finite-size scaling. We find that these weak interactions produce tricritical points and first-order transitions at low temperatures, which are in good agreement with experiments for the structural order-order phase transitions. Furthermore, we predict a tricritical point and first-order transitions at low temperatures on the order-disorder branch of the phase diagram. We also present the phase diagram.