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

TL;DR

This paper demonstrates that the O(n) model as n approaches zero is described by a logarithmic conformal field theory, with explicit correlation functions exhibiting logarithmic singularities.

Contribution

It provides explicit forms of correlation functions in the n→0 limit, establishing a connection between the O(n) model and logarithmic conformal field theory.

Findings

Correlation functions have logarithmic singularities.

Explicit two-, three-, and four-point functions derived.

The O(n) model in the n→0 limit is described by logarithmic CFT.

Abstract

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.