Ferromagnetic ordering in the two-dimensional dipolar XY model -: art. no. 134430

We investigate the low-temperature phase of the two-dimensional dipolar XY model. Within the framework of the nonlinear sigma model we show that the dipolar XY model is renormalizable, despite the anisotropic character of the dipolar interaction. We predict a low-temperature phase with spontaneous magnetization governed by a low-temperature fixed point with infinite dipolar coupling. The critical fixed point shows nonlinear behavior, leading to unusual critical phenomena; e.g., the correlation length and spontaneous magnetization show exponential behavior instead of power laws. The nature and flow diagram of the ferromagnetic transition are strikingly similar to the Kosterlitz-Thouless transition. But while in the Kosterlitz-Thouless transition the exponential behavior is a consequence of the topological excitations, the predicted phenomena in the dipolar XY model are solely due to spin-wave excitations. In addition to the dXY model we introduce a whole class of long-range XY models showing such nonstandard behavior. Parametrizing the divergences in terms of the correlation length we calculate the critical exponents of the transition. These exponents are correct in any loop order. The influence of topological excitations on the ferromagnetic transition is discussed.