Critical exponents of the O(N) model in the infrared limit from functional renormalization

TL;DR

This paper calculates the critical exponent nu for the O(N) model using functional renormalization group methods, revealing infrared fixed points and scaling behaviors relevant to phase transitions in various dimensions.

Contribution

It introduces a novel approach to determine the critical exponent nu via the infrared correlation length derived from the functional renormalization group.

Findings

Identifies an infrared fixed point in the broken phase of the O(N) model.

Shows the IR scaling behavior explains both 3D Ising and 2D Kosterlitz-Thouless transitions.

Demonstrates the correlation length can be dynamically generated from degeneracy in the RG flow.

Abstract

We determined the critical exponent $\nu$ of the scalar O(N) model with a strategy based on the definition of the correlation length in the infrared limit. The functional renormalization group treatment of the model shows that there is an infrared fixed point in the broken phase. The appearing degeneracy induces a dynamical length scale there, which can be considered as the correlation length. It is shown that the IR scaling behavior can account either for the Ising type phase transition in the 3-dimensional O(N) model, or for the Kosterlitz-Thouless type scaling of the 2-dimensional O(2) model.