An Eigenvalue Problem Related to the Nonlinear sigma Model:Analytical and Numerical Results Auteur(s): Fateev V., Onofri E. (Article) Publié: Journal Of Physics A: Mathematical And Theoretical, vol. 36 p.11881 - 1 (2003) Texte intégral en Openaccess : Ref HAL: hal-00266348_v1 Ref Arxiv: math-ph/0307010 DOI: 10.1088/0305-4470/36/47/014 WoS: 000188194800016 Ref. & Cit.: NASA ADS Exporter : BibTex | endNote 5 Citations Résumé: An eigenvalue problem relevant for the non-linear sigma model with singular metric is considered. We prove the existence of a non-degenerate pure point spectrum for all finite values of the size R of the system. In the infrared (IR) regime (large R) the eigenvalues admit a power series expansion around the IR critical point R → ∞. We compute high order coefficients and prove that the series converges for all finite values of R. In the ultraviolet (UV) limit the spectrum condenses into a continuum spectrum with a set of residual bound states. The spectrum agrees nicely with the central charge computed by the thermodynamic Bethe ansatz method. |