Two-Dimensional XY Ferromagnet Induced by Long-Range Interaction

The crossover between short-range and long-range (LR) universal behaviors remains a central theme in the physics of LR interacting systems. The competition between LR coupling and the Berezinskii-Kosterlitz-Thouless mechanism makes the problem more subtle and less understood in the two-dimensional (2D) XY model, a cornerstone for investigating low-dimensional phenomena and their implications in quantum computation. We study the 2D XY model with algebraically decaying interaction \sim\!\!1/r^2+\sigma. Utilizing an advanced update strategy, we conduct LR Monte Carlo simulations of the model up to a linear size of L=8192. Our results demonstrate continuous phase transitions into a ferromagnetic phase for \sigma < 2, which exhibit the simultaneous emergence of a long-ranged order and a power-law decaying correlation function due to the Goldstone mode. Furthermore, we find logarithmic scaling behaviors in the low-temperature phase at \sigma = 2. The observed scaling behaviors in the low-temperature phase for \sigma \le 2 agree with our theoretical analysis. Our findings request further theoretical understanding and can be of practical application in cutting-edge experiments like Rydberg atom arrays.