  The fourth-order cumulant of the magnetization, the Binder cumulant, is
determined at the phase transition of Ising models on square and triangular
lattices, using Monte Carlo techniques. Its value at criticality depends
sensitively on boundary conditions, details of the clusters used in calculating
the cumulant, and symmetry of the interactions or, here, lattice structure.
Possibilities to identify generic critical cumulants are discussed.
