DILUTE ANTIFERROMAGNETS - IMRY-MA ARGUMENT, HIERARCHICAL MODEL, AND EQUIVALENCE TO RANDOM-FIELD ISING-MODELS

We discuss some aspects of the problem of the equivalence of dilute an tiferromagnets and random field Ising models. We first investigate for dilute antiferromagnets the validity of the arguments of Imry and Ma. It turns out that they are applicable, but some care is required conc erning the role played by the so-called internal Peierls contours. Nex t we consider a hierarchical version of a dilute antiferromagnetic Isi ng model in the presence of a uniform magnetic field and show that a r enormalization group transformation maps it exactly into a hierarchica l version of the random field Ising model, thus proving their equivale nce as far as the critical behavior is concerned. In particular this i mplies that phase transition with spontaneous magnetization occurs onl y for dimension d > 2. Finally we show that in the absence of internal Peierls contours both models, in their hierarchical versions, exhibit phase transition already in dimension d = 2.