Local critical behaviour at impurities in Ising-type systems

We study the critical behaviour of the hyperfine field hH which is observed to depend on the probing atom and to differ from the bulk. A classical Ising-type model is used where the probing atom is assumed to change locally the pair interaction. The quantities determining hH are expressed in terms of higher order correlation functions of the unperturbed problem. Using a result of Lebowitz for ferromagnetic pair interaction, it is shown that in the true critical temperature range hH should show the same critical behaviour as in the bulk. This holds also in the presence of impurities and finite impurity concentration. Based on identities satisfied by the correlation functions obtained through a spin decoupling operation it is conjectured that the above result also holds for mixed and finite ranged interaction. An explanation of the experimental results for Ni is attempted.