Abstract
The critical behaviour of a magnetic system with O(N) spin symmetry, bounded by two (d-1)-dimensional hyperplanes meeting at an angle alpha , is studied within mean field theory and in d=4- epsilon dimensions. New exponents emerge for correlation functions, and magnetisation and susceptibilities, for spins close to the edge. They can be expressed in terms of known bulk and surface exponents, together with a single new edge exponent which depends, however, on the angle alpha . This exponent is computed to first order in epsilon .