Absence of Asymptotic Freedom in Non-Abelian Models

Details Absence of Asymptotic Freedom in Non-Abelian Models Absence of Asymptotic Freedom in Non-Abelian Models

2000-02-18

arxiv.org/abs/hep-th/0002153v1

Physics

High Energy Physics

High Energy Physics - Theory

4 pages, 4 figures

Scientific paper

The percolation properties of equatorial strips of the two dimensional O(3) nonlinear $\sigma$ 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.

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