Finite Temperature Transitions in 2D Dipolar Systems with Uniaxial Anisotropy

We discuss the finite temperature transitions of 2D dipoles with short range exchange ( $J$), long range dipolar ( $g$), and $z$-axis anisotropy ( $K$) interactions. Under some conditions there can be three transitions so that at low temperatures only the $z$ magnetization $M_z$ is nonzero. As the temperature is increased, (1) $M_x$ becomes nonzero. Eventually, (2) $M_z$ becomes zero and then (3) $M_x$ becomes zero. We discuss renormalization group, mean field, and Monte Carlo calculations for this system. Possible relevance of this to recent experimental results on ultrathin magnetic films is discussed.