Local magnetisation of the n-vector model with a large-scale defect in the limit n to infinity

Abstract

The local magnetisation of the three-dimensional n-vector model is studied near the large-scale d'-dimensional defect in the limit n to infinity . The model is characterised by the fact that the spin lengths close to the defect are changed as Sr2=n(1- lambda /r) with the distance r from the defect. It is shown that near the critical point the local magnetisation exhibits a nonuniversal behaviour if d'=0, 1 and a nonscaling behaviour if d'=2. In the first case the critical exponents beta ' and nu ' are calculated up to the order of lambda and it is shown that these exponents satisfy the usual scaling law relations up to this order.