  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 analyze 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 behavior of the XY model
is fully compatible with the Kosterlitz-Thouless scenario. Finite size effects
have to be dealt with by using great care in order to discern among two very
different physical pictures that can look very similar if analyzed without
large attention.
