Two‐dimensional XY magnets with annealed non‐magnetic impurities

The global phase diagram of a vectorial generalization of the Blume‐Emery‐Griffiths model is obtained using Migdal’s approximate renormalization procedure. Classical two‐component spins and non‐magnetic impurities populate a triangular lattice, with nearest‐neighbor interactions. The phase diagram in thermodynamic field space is divided into magnetic and impurity‐rich phases by a first‐order surface of discontinuous impurity concentrations, terminating in an Ising‐type critical line. The magnetic region is further divided into a high‐temperature paramagnetic phase and a low‐temperature Kosterlitz‐Thouless phase. The exponent η=1/4 of the pure system is preserved at the higher‐order surface separating these two phases. This surface terminates in a line of critical end‐points on the first‐order surface, and, consequently, no tricritical point occurs for any values of the model parameters. However, the Ising critical line and the line of critical end‐points approach each other in a certain limit, yielding an effective tricritical phase diagram. Within the Kosterlitz‐Thouless phase, lines of constant η bunch together as the effective tricritical point is approached, in apparent agreement with tricritical scaling. This is also a model for superfluidity and phase separation in helium films.