Field-induced transitions and spatial chaos in the classical XY spin chain

We study the lowest-lying excitation of a classical ferromagnetic XY spin c hain, in the presence of a symmetry breaking magnetic held. Extremizing the energy of this system leads to a two-dimensional nonlinear map, whose allo wed phase space shrinks with increasing field in a nontrivial manner. The o rbits of the map represent the set of extremum energy spin configurations. For each field, we compute the energy of the members of this set and find t he lowest energy among them, excluding the obvious ground state configurati on with all spins parallel along the held direction. This state turns out t o be the unstable fixed point of the map. We show that up to a certain (pri mary) critical field, a separatrixlike 2 pi soliton configuration is the lo west-energy excitation, with an energy very close to the ground state energ y. For any field beyond this critical field, the soliton disappears and low est excitation is a librational configuration corresponding to the outermos t orbit in the phase plot at that field. Further, its energy is found to be much higher than the ground state energy, leading to a sharp jump in the d ifference in energy between the former and the latter at this field. With f urther increase in the field, sharp jumps in the excitation energy arise at certain secondary critical fields as well. We show that these appear when the corresponding spin configurations become commensurate. This complex beh avior of the energy is interpreted and its effect on the magnetization and static susceptibility of the system is also studied.