Critical correlation susceptibility relation in random-field systems

We develop a technique by which systematic corrections (also including corrections to local-mean-field equations) to a simple relation between the average spin and the external field may be obtained. We find that the relative corrections to 〈${\phi }_q$〉=-${\chi }_q$ $h_q$ (${\chi }_q$ being the susceptibility in the presence of the field) are vanishingly small for small q’s at an assumed continuous transition. We find a relation between the divergence of the susceptibility and correlation function.