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Absence of Asymptotic Freedom in Non-Abelian Models

A. Patrascioiu·E. Seiler
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Abstract

The 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.

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A. Patrascioiu, E. Seiler. 2000-02-18. Absence of Asymptotic Freedom in Non-Abelian Models. https://arxiv.org/abs/hep-th/0002153

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