Phi4tools: Compilation of Feynman diagrams for Landau-Ginzburg-Wilson theories

Abstract

Scalar field theories with quartic interactions are of central interest in the study of second-order phase transitions. For three-dimensional theories, numerous studies make use of the fixed-dimensional perturbative computation of [B. Nickel, D. Meiron, and G. Baker Jr, Compilation of 2-pt and 4-pt graphs for continuous spin model, University of Guelph report (1977)], unfortunately left unpublished. We independently verify the results of Nickel et al., and we extend the computation to the eighth order in the coupling constant. The results of our calculations, together with the tools developed, are made available in Phi4tools, a user-friendly package that allows displaying the information about the individual Feynman diagrams, including the numerical values for the diagrams for zero, two, and four-point functions. We also provide the perturbative series up to order eight for the renormalization-group functions for the $O(N)$ and cubic anisotropic models.

v2: 30 pages, 6 figures; added figure 2 and section 2.7 plus other minor improvements. Matches published version. The package can be found at https://resources.wolframcloud.com/PacletRepository/resources/GSberveglieri/Phi4tools

References in corpus (11)

• Algorithm FIRE -- Feynman Integral REduction
• Integral Reduction with Kira 2.0 and Finite Field Methods
• The critical exponents of the superfluid transition in He4
• Bootstrapping Heisenberg Magnets and their Cubic Instability
• Bose-Einstein Condensation Temperature of Homogenous Weakly Interacting Bose Gas in Variational Perturbation Theory Through Seven Loops
• Six-loop $\epsilon$ expansion study of three-dimensional $n$-vector model with cubic anisotropy
• $\text{tapir}$: A tool for topologies, amplitudes, partial fraction decomposition and input for reductions
• Tropical Feynman integration in the Minkowski regime
• Self-Dualities and Renormalization Dependence of the Phase Diagram in 3d $O(N)$ Vector Models
• Renormalised four-point coupling constant in the three-dimensional O(N) model with N=0
• Critical behavior of isotropic systems with strong dipole-dipole interaction: three-loop study

Cited by in corpus (1)

• Tropicalized quantum field theory and global tropical sampling