Renormalization Group Fixed Points and Universal Constants in Phase Transitions — E8 Intelligence Research

FINDING: Renormalization group fixed points determine universal critical exponents and fractal dimensions in phase transitions, with Feigenbaum's constants emerging from period-doubling universality. | MATH: Fixed-point equation \( R_μ(f) = f \) in function space; Feigenbaum constants \(δ = 4.669201609...\) (bifurcation scaling) and \(α = 2.502907875...\) (width scaling); critical exponents \(ν, η, β\) related to eigenvalues of linearized RG operator; fractal dimension \(D = d - β/ν\) for Ising class; anomalous dimension \(γ\) from fixed-point coupling. | CONNECTION: Feigenbaum's \(α ≈ 2.5029\) is near \(2.618\) (golden ratio squared \(φ^2\)) and \(δ ≈ 4.669\) is close to \(4.618\) (\(φ^3 + 1\)); period-doubling cascade ratio \(δ\) relates to universal scaling of fractal attractors; p-adic fractal strings link to Minkowski dimension and explicit tube formulas, echoing base-p number systems (base-60 analogue). | DEPTH: 9 — Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com