Finite-temperature ordering in two-dimensional magnets

We study the two-dimensional quantum Heisenberg antiferromagnet on the squa re lattice with easy-axis exchange anisotropy. By the semiclassical method called pure-quantum self-consistent harmonic approximation we analyze sever al thermodynamic quantities and investigate the existence of a finite tempe rature transition, possibly describing the low-temperature critical behavio r experimentally observed in many layered real compounds. We find that an I sing-like transition characterizes the model even when the anisotropy is of the order of 10(-2)J (J being the intralayer exchange integral), as in mos t experimental situations. On the other hand, typical features of the isotr opic Heisenberg model are observed for both values of anisotropy considered , one in the quasi-isotropic limit and the other in a more markedly easy-ax is region. The good agreement found between our theoretical results and the experimental data relative to the real compound Rb2MnF4 shows that the ins ertion of the easy-axis exchange anisotropy, with quantum effects properly taken into account, provides a quantitative description and explanation of the experimental data, thus allowing us to recognize in such anisotropy the main agent for the observed onset of finite temperature long-range order.