Tensor Nonclosure in Dipolar Functional Renormalization Group Flows: Python Code and Numerical Data

Abstract

This repository contains the numerical software, reference datasets, validation procedures, and figure-generation scripts accompanying the research manuscript “Tensor Nonclosure in Momentum-Dependent Functional Renormalization Group Flows for Dipolar Criticality: Analytic Bounds and Reproducible Numerical Benchmarks” by Harshil Soni. The work investigates the momentum dependence of functional renormalization group (FRG) flows in a three-component dipolar critical theory, with particular emphasis on the generation of tensor structures that cannot be represented by restricted scalar momentum-dependent truncations. The archive supports numerical investigations of finite-momentum two-point functions, transverse polarization splitting, tensor-sector nonclosure, and momentum-dependent projected closures. It includes implementations of numerical FRG calculations, fixed-point analyses, tensor projection routines, exact spherical angular-moment calculations, radial coefficient evaluations, and regulator-dependent comparisons. The accompanying reference datasets support comparisons between analytical calculations and numerical integration, including momentum-dependent polarization differences, quadrature convergence, fixed-point consistency, and the accuracy of alternative momentum-closure approximations. Additional validation scripts test algebraic identities, geometric symmetries, numerical convergence, and consistency with established analytical radial bounds. The archive also contains scripts for regenerating the four manuscript figures, including polarization benchmarks, tensor nonclosure, numerical quadrature convergence, and momentum-dependent closure comparisons. The numerical checks provide reproducible evidence for the analytical and computational results presented in the manuscript. Numerical convergence tests of the three-dimensional small-momentum limit are distinguished from a complete mathematical proof of that limit. Contents: Python source code, numerical reference data (CSV/JSON/NPZ), validation and regression tests, figure-generation scripts, dependency specifications, README documentation, citation metadata, and licensing information. Author: Harshil Soni Associated manuscript: Tensor Nonclosure in Momentum-Dependent Functional Renormalization Group Flows for Dipolar Criticality: Analytic Bounds and Reproducible Numerical Benchmarks (2026). Version: 1.0.0 This archive supports computational transparency, independent verification, and reproducibility of the numerical results reported in the accompanying manuscript. Certain archived numerical checkpoints are preserved as reference inputs rather than regenerated entirely from first principles by the included scripts.