Criticality of the O(N) universality via global solutions to nonperturbative fixed-point equations

• Published in: The European physical journal. C, Particles and fields Particles and fields, 2024-09, Vol.84 (9), p.897-12, Article 897
• Main Authors: Tan, Yang-yang, Huang, Chuang, Chen, Yong-rui, Fu, Wei-jie
• Format: Article
• Language: English
• Subjects: Approximation; Astronomy; Astrophysics and Cosmology; Asymptotic methods; Asymptotic properties; Asymptotic series; Behavior; Continuity (mathematics); Critical phenomena; Eigenvalues; Eigenvectors; Elementary Particles; Hadrons; Heavy Ions; Initial conditions; Measurement Science and Instrumentation; Nuclear Energy; Nuclear Physics; Phase transitions; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Regular Article - Theoretical Physics; String Theory; Taylor series
• ISSN: 1434-6052; 1434-6044; 1434-6052
• DOI: 10.1140/epjc/s10052-024-13291-7

Fixed-point equations in the functional renormalization group approach are integrated from large to vanishing field, where an asymptotic potential in the limit of large field is implemented as initial conditions. This approach allows us to obtain a global fixed-point potential with high numerical accuracy, that incorporates the correct asymptotic behavior in the limit of large field. Our calculated global potential is in good agreement with the Taylor expansion in the region of small field, and it also coincides with the Laurent expansion in the regime of large field. Laurent expansion of the potential in the limit of large field for general case, that the spatial dimension d is a continuous variable in the range 2 ≤ d ≤ 4 , is obtained. Eigenfunctions and eigenvalues of perturbations near the Wilson–Fisher fixed point are computed with the method of eigenperturbations. Critical exponents for different values of d and N of the O ( N ) universality class are calculated.