The Binder cumulant was introduced by Kurt Binder in the context of finite size scaling. It is a quantity that is supposed to be invariant for different system sizes at criticality. For an Ising model with zero field, is given by
where m is the order parameter. It is therefore a fourth order cumulant, related to the kurtosis.
In the thermodynamic limit, where the system size , for , and for . Thus, the function is discontinuous in this limit --- the useful fact is that curves corresponding to different system sizes (which are, of course, continuous) all intersect at approximately the same temperature, which provides a convenient estimatation of the critical temperature.