Random magnetic fields in the n-vector model: the large-n limit

Abstract

The authors solve exactly the large-n limit of the n-vector model with a quenched random field, allowing for the possibilities of both long-range correlations in the random field and long-range exchange interactions. It should be emphasised that, although the ideal Bose gas is frequently assumed identical to the large-n limit of the n-vector model, their identity has only been demonstrated for models with full translational symmetry (Gunton and Buckingham 1968, Stanley 1968). Indeed, without such symmetry, there are examples where several kinds of chemical potential must be introduced into the Bose gas in order to preserve the relationship with the n-vector model (Knops 1973, Fishman and Ziman 1982). In fact, the authors find that the two models behave equivalently. In addition, they are able to extend earlier results in the various ways necessary to present a comparison of the large-n limit with recent work (Chang and Abrahams 1984, Kardar et al. 1983) using epsilon -expansions about the lower and upper critical dimension some discrepancies emerge.