Nature of the "Griffiths" Singularity in Dilute Magnets

The nature of the singular behavior pointed out by Griffiths for H=0 in dilute magnets is investigated. It is argued that for concentration p less than that for formation of an infinite cluster, all derivatives of M(H) are finite. The nonanalyticity in M(H) is due to a branch cut along the imaginary H axis having weight exp[−(const)/|H|] for |H|→0, and is thus too weak to be experimentally observable. Some numerical and exact analytic results for the dilute magnet on a Bethe lattice are presented.