Test of asymptotic freedom and scaling hypothesis in the 2d O(3) sigma model

Abstract

The 7--particle form factors of the fundamental spin field of the O(3) nonlinear $\sigma$--model are constructed. We calculate the corresponding contribution to the spin--spin correlation function, and compare with predictions from the spectral density scaling hypothesis. The resulting approximation to the spin--spin correlation function agrees well with that computed in renormalized (asymptotically free) perturbation theory in the expected energy range. Further we observe simple lower and upper bounds for the sum of the absolute square of the form factors which may be of use for analytic estimates.

arXiv comment14 pages, 3 figures, latex

References in corpus (6)

• From Form Factors to Correlation Functions: The Ising Model
• Off-Shell Dynamics of the O(3) Nonlinear Sigma-Model -- Beyond Monte-Carlo and Perturbation Theory
• Comparison of the O(3) Bootstrap $\sigma$-Model with the Lattice Regularization at Low Energies
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Cited by in corpus (4)

• Structure functions of the 2d O(n) non-linear sigma models
• Structure functions of 2d integrable asymptotically free models
• Asymptotic Freedom and Finite-size Scaling of Two-dimensional Classical Heisenberg Model
• Thermodynamic Bethe ansatz for the AII sigma-models