Is the 2D O(3) Nonlinear $\sigma$ Model Asymptotically Free?

Abstract

We report the results of a Monte Carlo study of the continuum limit of the two dimensional O(3) non-linear $\sigma$ model. The notable finding is that it agrees very well with both the prediction inspired by Zamolodchikovs' S-matrix ansatz and with the continuum limit of the dodecahedron spin model. The latter finding renders the existence of asymptotic freedom in the O(3) model rather unlikely.

10 pages

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Cited by in corpus (16)

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• Off-Shell Dynamics of the O(3) Nonlinear Sigma-Model -- Beyond Monte-Carlo and Perturbation Theory
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• Correction to four-loop RG functions in the two-dimensional lattice O(n) $\sigma$-model
• Unexpected results in asymptotically free quantum field theories
• Asymptotically free models and discrete non-Abelian groups
• The classical two-dimensional Heisenberg model revisited: An $SU(2)$-symmetric tensor network study
• Qubitization strategies for bosonic field theories
• Fuzzy gauge theory for quantum computers
• A probabilistic mechanism for quark confinement
• Asymptotically free theories based on discrete subgroups
• Universality of a truncated sigma-model
• Nonlinear $\sigma$-model, form factors and universality
• Discrete Symmetry Enhancement in Nonabelian Models and the Existence of Asymptotic Freedom
• Spin models on Platonic solids and asymptotic freedom
• Fluctuations of topological charges in two-dimensional classical Heisenberg model