A numerical study of the RG equation for the deformed O(3) nonlinear sigma model Original Research Article

The Renormalization Group equation describing the evolution of the metric of the nonlinear sigma model poses some nice mathematical problems involving functional analysis, differential geometry and numerical analysis. In this article we briefly report some results obtained from the numerical study of the solutions in the case of a two-dimensional target space (deformation of the O(3) σ-model In particular, our analysis shows that the so-called sausages define an attracting manifold in the U(1)-symmetric case, at one-loop level. Moreover, data from two-loop evolution are used to test the association (Fateev, Onofri and ALB. Zamolodchikov, Nucl. Phys. B 406 (1993) 521) between the so-called SSMη field theory and a certain U(1)-symmetric, factorized scattering theory (FST).