Nontrivial fixed point in nonabelian models

TL;DR

This paper studies the percolation behavior of equatorial strips in the 2D O(3) nonlinear sigma model, showing that narrow strips do not percolate at low temperatures, implying a massless phase and absence of asymptotic freedom.

Contribution

It provides evidence that equatorial strips do not percolate at low temperatures and links this to the vanishing mass gap and non-asymptotic freedom in the model.

Findings

Equatorial strips do not percolate at low temperatures.

Vanishing mass gap at low temperature.

Absence of asymptotic freedom in the continuum limit.

Abstract

We investigate the percolation properties of equatorial strips in the two-dimensional O(3) nonlinear $\sigma$ model. We find convincing evidence that such strips do not percolate at low temperatures, provided they are sufficiently narrow. Rigorous arguments show that this implies the vanishing of the mass gap at low temperature and the absence of asymptotic freedom in the massive continuum limit. We also give an intuitive explanation of the transition to a massless phase and, based on it, an estimate of the transition temperature.