Spin-ice phase in a modified XY model

We study a modified XY model on the square lattice with magnetic and nematic nearest-neighbor interactions among classical spins that has been introduced earlier [ D. H. Lee and G. Grinstein, Phys. Rev. Lett. 55, 541 (1985); S. E. Korshunov, JETP Lett. 41, 263 (1985)]. We concentrate on the previously unexplored case of competing magnetic and nematic interactions. Using a combination of Monte Carlo simulations and of finite-size scaling, we show that the phase diagram of the model contains, in addition to the previously studied paramagnetic, ferromagnetic, and nematic phases, also a spin-ice-like phase. The individual phases can be classified making use of a close relation between the continuous XY model and a discrete 16-vertex model.