phi4-one-loop-beta-repro

Reproducible derivation and numerical cutoff verification of the one-loop beta function in Euclidean scalar φ⁴ theory.

This repository accompanies the manuscript: “A reproducible derivation of the one-loop β(λ) function in Euclidean φ⁴ theory with numerical cutoff verification.”

Contents

• notebooks/numerical_cutoff_verification.ipynb — computes the cutoff integral, performs the fit-window robustness check, and generates the plots.
• figures/Fig1_I_vs_logLambda2.pdf — (I(\Lambda,m)) vs (\ln(\Lambda^2/m^2)) with linear fit.
• figures/Fig2_Delta_vs_invLambda2.pdf — residual (\Delta(\Lambda)) vs (1/\Lambda^2) with asymptote.

Reproduce the figures

Python + pip (recommended)

python -m venv .venv
# activate:
# Windows: .venv\Scripts\activate
# Linux/macOS: source .venv/bin/activate
pip install -r requirements.txt