Influence of long range forces in isotropic two-dimensional magnetism

The two-dimensional XY model presents a magnetic phase transition with non vanishing long range order parameter if the range of the interactions is long enough. This fact is exhibited, within a variational framework, on the classical XY model by assuming an exchange integral decaying as R- sup(2+p) for long distances. Long range magnetic order appears if p<2. The isothermal susceptibility is also discussed