are known for those models. 10,11 Note first the presence of a non-unique ground state with non-trivial continuous degeneracy that is typical both for three-dimensional lattices 11 and for two-dimensional lattices of planar 12,13 and three-dimensional dipoles. 14 Two-dimensional systems of Ising-type dipoles with perpendicular anisotropy demonstrate a complicated be- havior when subject to an external magnetic field perpendicular to the array’s plane. 15 At zero field, the ground state of a square 2D array is chessboard antiferromagnetic (AFM), and this state is stable at low fields H < H$_{1}$ = 2 . 3 M , where M = m$_{0}$/a 3 is characteristic field of magnetic dipole interaction, and a is the lattice spacing. The ferromagnetic (FM) (sat- urated) state is stable at high fields H > H$_{0}$ = 9 . 03 M , with a cascade of phase transitions between complicated magnetic structures at H$_{1}$ < H < H$_{0}$ . The models 10–12 were discussed originally in regard to the description of real crystalline spin systems in which the dipolar interaction is predominant, such as some rare-earth mag- nets. However, fabrication and experimental study of magnetic dot arrays provide new physical systems for the testing of basic magnetism models. For many materials, such as compounds with rare-earth ions, granular magnets, and diluted solid solution of paramag- netic ions in nonmagnetic crystals, the magnetic properties seem to be similar to those of dot arrays. Nevertheless, magnetic dot lattices exhibit physical properties, which are absent in all above-mentioned systems. First, dot arrays in contrast to layered crystals are literally two-dimensional. The manifestations of long-ranged magnetic dipole interaction are princi- pally different for of layered crystals and truly two-dimensional systems. 16 Second, the scale of dipolar interaction of two spins (2 µ$_{B}$S ) $^{2}$/a$^{3}$, where µ$_{B}$ the Bohr magneton, a is the inter- spin distance, even with large spins like S = 7 / 2 does not exceed several Kelvins, whereas for dots with volume as small as 10 4 nm 3 the characteristic magnetic moment m$_{0}$ > 10 $^{3}$µ$_{B}$ S , and the characteristic energy can be comparable to or even higher than the thermal energy at room temperature. Besides, for a compound with high density of rare earth ions though the exchange interaction is small it is not completely negligible. As both FM and AFM exchange interactions of adjacent spins lead to magnetic states essentially different from those caused by dipolar interaction, these systems can not be considered as purely dipolar. The large magnetic moment of each particle is typical also for granular materials, but the magnetic dot lattices are different from the latter by the high spatial regularity. It is worth mentioning a new class of materials – molecular crystals with high-spin molecules. 17 However, they are three-dimensional, and the spin of these systems is 3