An analytic study of the friedel criterion in disordered magnetic states in transition metals in the presence ofS-D hybridisation,using the cluster bethe lattice approach

In this paper we present a new theory for including both short range order and long range order simultaneously in the well known cluster Bethe lattice method for binary alloys. We have used this theory for obtaining the Friedel criterion for the appearance of magnetic moments in disordered states using the single band Hubbard model. This is followed by a study of this criterion in a two-bands-d hybridised Hubbard model, which is considered as a simulation of real transition metals. A new technique for solving this problem in the Bethe lattice network is presented, which yields an analytic solution for the critical correlation strength in the presence of hybridisation and short range order. It is found that in all cases hybridisation tends to diminish the tendency for magnetisation, which is in accord with physical expectations.