2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/49872The percolation properties of equatorial strips of the two dimensional O(3) nonlinear $σ$ model are investigated numerically. Convincing evidence is found that a sufficently narrow strip does not percolate at arbitrarily low temperatures. Rigorous arguments are used to show that this result implies both the presence of a massless phase at low temperature and lack of asymptotic freedom in the massive continuum limit. A heuristic estimate of the transition temperature is given which is consistent with the numerical data.4 pages, 4 figuresHigh Energy Physics - TheoryHigh Energy Physics - LatticeMathematical Physicstext