Renormalisation group calculations of the critical exponents of the n-vector model with a free surface

Abstract

The correlation function critical exponents eta /sub /// and eta perpendicular to of the semi-infinite phi 4 model with O(n) symmetry have been calculated to order epsilon 2 for the ordinary and special transitions. The results for the ordinary transition are inconsistent with the relation gamma 11= nu -1 proposed by Bray and Moore (1977). Comparisons with series expansion results in two and three dimensions are presented for n=0 and n=1.