Ground state of the one-dimensional chiral XY model in a field

We consider a one-dimensional system of classical planar spins with nearest-neighbor chiral interactions in the presence of a magnetic field. The phase diagram of the model at zero temperature is studied with use of the method of effective potentials and other numerical and analytical techniques. In contrast to the Frenkel-Kontorova model, the interaction potential between spins is not strictly convex, and this leads to some qualitatively different behavior. Among other interesting features, we find a succession of first-order transitions, sequences of triple points and their accumulation points, and points where the ground state is infinitely degenerate.