  The problem of magnetic transitions between the low-temperature (macrospin
ordered) phases in 2D XY arrays is addressed. The system is modeled as a plane
structure of identical single-domain particles arranged in a square lattice and
coupled by the magnetic dipole-dipole interaction; all the particles possess a
strong easy-plane magnetic anisotropy. The basic state of the system in the
considered temperature range is an antiferromagnetic (AF) stripe structure,
where the macrospins (particle magnetic moments) are still involved in
thermofluctuational motion: the superparamagnetic blocking $T_b$ temperature is
lower than that ($T_\text{af}$) of the AF transition. The description is based
on the stochastic equations governing the dynamics of individual magnetic
moments, where the interparticle interaction is added in the mean field
approximation. With the technique of a generalized Ott-Antonsen theory, the
dynamics equations for the order parameters (including the macroscopic
magnetization and the antiferromagnetic order parameter) and the partition
function of the system are rigorously obtained and analysed. We show that
inside the temperature interval of existence of the AF phase, a static external
field tilted to the plane of the array is able to induce first order phase
transitions from AF to ferromagnetic state; the phase diagrams displaying
stable and metastable regions of the system are presented.
