Critical and tricritical points near the Potts model transition of uniaxially stressed SrTiO₃

The authors study the phase diagrams of SrTiO₃ as function of temperature and of uniaxial stress along a general direction. In particular, new results are presented for stress along (110) and along (1+ delta , 1+ delta , 1-2 delta ). In the latter case, the trigonal pseudotetragonal phase transition is described by a three-state Potts model Hamiltonian with both quadratic and linear symmetry-breaking fields. Far away from the (zero-stress) multicritical point, the leading fluctuations are described by the underlying XY model. The first-order Potts model transition is turned second order by the symmetry-breaking fields via a tricritical point, at delta _t(<0), and at a critical point, delta _c(>0). The universal ratio delta _t/ delta _c is calculated to order epsilon =4-d. In the close vicinity of the multicritical point, the XY model underlying all of these results undergoes a crossover to a Gaussian model, and the Potts line approaches the temperature axis tangentially.