Incommensurability in the frustrated two-dimensional $\mathrm{XY}$ model

To examine the properties of the frustrated $\mathrm{XY}$ model at an incommensurate field we have examined a sequence of magnetic filling factors f which approach the irrational value of one minus the golden mean. At all f studied, the system undergoes a finite-temperature ordering transition involving the freezing out of Ising-like domain walls. As one approaches incommensurability, the low-temperature phase of the system changes from the staircase states found by Halsey [Phys. Rev. B 31, 5728 (1984); J. Phys. C 18, 2437 (1985)] to a striped phase consisting of a superlattice of parallel shift (Pott’s-like) domain walls. Our results suggest that the glassy effects previously reported for this model are an artifact of the boundary conditions and dynamics that were used.