Spin-Level Hybridization between Ising and XY Models: A Monte Carlo Study

We develop a classical spin model by hybridizing the well studied Ising and XY models at the spin level. We investigate the phase transition and the critical phenomena of a clean two-dimensional system of this XY-Ising hybrid spin model by means of large-scale Monte Carlo simulations. Preliminary results suggest that the order phase is purely Ising-like and a ferromagnetic phase transition occurs at a critical temperature ($T_c\simeq 1.7$) smaller than that of the clean two-dimensional Ising model ($T_{c}^{Ising}\simeq 2.269$). This phase transition is accompanied by the formation of Ising ferromagnetic domains confined by energetically cheap XY walls (Ising-XY ferromagnetic domains). This picture of domains persists for significantly high temperatures producing a novel paramagnetic phase. By increasing the temperature in this paramagnetic phase, the Ising-XY ferromagnetic domains do not completely transform into Ising-like paramagnetic domains or a globally mixed paramagnetic bulk phase but rather they undergo a continuous splitting into smaller ones. We also investigate the critical properties of our system in detail and compare them to those of the clean parent models and their universality classes.