Random Fields Generated by Dilution in Zero External Field

It is shown that arbitrarily small amounts of bond or site dilution generate (in zero magnetic field) effects in some Ising antiferromagnets much like random fields and are, therefore, not covered by the criterion of Harris. All antiferromagnets on f.c.c. lattices as well as antiferromagnets of type-II in b.c.c. lattice suffer this effect. We argue that the cross-over exponent into the impurity-dominated regime fulfills in any dimensionality, and that an Ising model is unstable against any small site or bond dilution. Numerical results for strips, obtained by the transfer matrix method confirm this picture