Dynamics in the anisotropic XY model driven by dichotomous Markov noise.

The statistics of a subcritical spatially homogeneous XY spin system driven by dichotomous Markov noise as an external field is investigated, particularly focusing on the switching process of the sign of the order parameter parallel to the external field. The switching process is classified in two types, which are called the Bloch-type switching and the Ising-type switching, according to whether or not the order parameter perpendicular to the external field takes finite value at the switching. The phase diagram for the onset of the switching process with respect to the amplitude of the external field and the anisotropy parameter of the system is constructed. It is revealed that the power spectral density I(omega) for the time series of the order parameter in the case of the Bloch-type switching is proportional to omega(-32) in an intermediate region of omega. Furthermore, the scaling function of I(omega) near the onset point of the Bloch-type switching is derived.