Multiple pseudo-plateaux states and antiferromagnetic pair selection in the XY model in the highly frustrated honeycomb lattice.

We present a study of the low temperature magnetic phases of the classical $XY$ model with third nearest neighbor interactions on the honeycomb lattice at the maximally frustrated point under an external magnetic field by extensive Monte Carlo simulations. We focus on the characterization of the emergent low temperature phases, which are a direct consequence of the unusually high numbers of spins per plaquette in the model. Specifically, we show that, since thermal fluctuations partially lift the ground-state degeneracy and select the most collinear states, the selected states are those with the highest number of ``antiferromagnetic pairs'' (AFp) compatible with the exernal magnetic field. These AFp are formed in such a way that they maximize the degeneracy of the selected submanifold of ground states. Moreover, two collinear pseudoplateaux emerge at $M=1/3$ and $M=2/3$. To characterize the magnetization process, we employ Monte Carlo simulations and calculate relevant order parameters to construct the complete temperature vs. magnetic field phase diagram.