3D spin glass and 2D ferromagnetic XY model: a comparison

We compare the probability distributions and Binder cumulants of the overlap in the 3D Ising spin glass with those of the magnetization in the ferromagnetic 2D XY model. We analyse similarities and differences. Evidence for the existence of a phase transition in the spin glass model is obtained thanks to the crossing of the Binder cumulant. We show, that the behaviour of the XY model is fully compatible with the Kosterlitz-Thouless scenario. Finite size effects have to be dealt with carefully in order to differentiate between two very different physical pictures that can look very similar.