XY criticality arising from emergent symmetry in the three-dimensional Ashkin-Teller model.

The Ashkin-Teller model plays a central role in studying the phase transitions of statistical mechanics models and condensed matter systems. Nevertheless, the phase transitions of the three-dimensional Ashkin-Teller model with competing interactions have long been an enigma. Here, we employ a methodology conceptually based on emergent symmetry and perform embedding cluster Monte Carlo simulations for unprecedentedly large systems. We find that the distribution of a two-dimensional magnetization vector displays emergent O(2) symmetry, which appears along the critical line separating the paramagnetic phase from the Baxter and mixed phases. Sign-reversal finite-size effects are visible in the deviations from O(2) symmetry, but the thermal and magnetic renormalization exponents are universally close to the exponents of the three-dimensional XY model. The newly unveiled "extraordinary-log" critical phase and "special" transition of the XY model are realized in a plane defect of the critical Ashkin-Teller model. Thus, for the three-dimensional Ashkin-Teller model, our study provides complementary evidence of an XY critical line, which arises from the emergence of O(2) symmetry.