Absence of Asymptotic Freedom in Non-Abelian Models

2000/02/18 by A. Patrascioiu, Adrian Patrascioiu, Patrascioiu, A. +3
Materials Science · Mathematics · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Theory (hep-th) #Material Dynamics and Properties #Mathematical Physics (math-ph) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #hep-lat #hep-th #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.hep-th/0002153

4 pages, 4 figures

arxiv created 2000/02/18 · openalex publication_date 2000/02/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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