Nontrivial fixed point in nonabelian models

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.