Nonlinear $\sigma$-model, form factors and universality

Abstract

We report the results of a very high statistics Monte Carlo study of the continuum limit of the two dimensional O(3) non-linear $\sigma$ model. We find a significant discrepancy between the continuum extrapolation of our data and the form factor prediction of Balog and Niedermaier, inspired by the Zamolodchikovs' S-matrix ansatz. On the other hand our results for the O(3) and the dodecahedron model are consistent with our earlier finding that the two models possess the same continuum limit.

10 pages, 5 figures

References in corpus (6)

• Off-Shell Dynamics of the O(3) Nonlinear Sigma-Model -- Beyond Monte-Carlo and Perturbation Theory
• Is the 2D O(3) Nonlinear $\sigma$ Model Asymptotically Free?
• Continuum Limit of $2D$ Spin Models with Continuous Symmetry and Conformal Quantum Field Theory
• A Scaling Hypothesis for the Spectral Densities in the O(3) Nonlinear Sigma-Model
• Does Conformal Quantum Field Theory Describe the Continuum Limits of 2D Spin Models with Continuous Symmetry?
• Comment on "Scaling Hypothesis for the Spectral Densities in the Nonlinear Sigma Model"

Cited by in corpus (6)

• Comparison of the O(3) Bootstrap $\sigma$-Model with the Lattice Regularization at Low Energies
• Unexpected results in asymptotically free quantum field theories
• Asymptotically free models and discrete non-Abelian groups
• Asymptotically free theories based on discrete subgroups
• Discrete Symmetry Enhancement in Nonabelian Models and the Existence of Asymptotic Freedom
• Spin models on Platonic solids and asymptotic freedom