The O(n) Model in the nto 0 Limit (self-avoiding-walks) and Logarithmic Conformal Field Theory

We consider the O(n) theory in the $n \to 0$ limit. We show that the theory is described by logarithmic conformal field theory, and that the correlation functions have logarithmic singularities. The explicit forms of the two-, three- and four-point correlation functions of the scaling fields and the corresponding logarithmic partners are derived.