2019/03/31 by Oleg Antipin, Jahmall Bersini
Mathematics · Physics and Astronomy · #Anisotropy #Computer science #Expression (computer science) #Geometry #Mathematical analysis #Mathematical physics #Mathematics #Mixing (physics) #Operator (biology) #Operator product expansion #Order (exchange) #Physics #Product (mathematics) #Pure mathematics #Quantum chaos and dynamical systems #Quantum mechanics #Spectrum (functional analysis) #Stochastic processes and statistical mechanics #Taylor series #Theoretical and Computational Physics #cond-mat.stat-mech #hep-ph #hep-th
paper · pdf · doi:10.1103/physrevd.100.065008
published as Phys. Rev. D 100, 065008 (2019) · 22 pages. Matches the published version
openalex publication_date 2019/09/16 · arxiv created 2019/09/18 · arxiv updated 2019/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We compute the spectrum of anomalous dimensions of nonderivative composite operators with an arbitrary number of fields n in the O(N) vector model with cubic anisotropy at the one-loop order in the \ensuremathε expansion. The complete closed-form expression for the anomalous dimensions of the operators which do not undergo mixing effects is derived, and the structure of the general solution to the mixing problem is outlined. As examples, the full explicit solution for operators with up to n=6 fields is presented and a sample of the operator product expansion coefficients is calculated. The main features of the spectrum are described, including an interesting pattern pointing to the deeper structure.