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 \( R_\mu(f) = f \) in function space; Feigenbaum constants \(\delta = 4.669201609...\) (bifurcation scaling) and \(\alpha = 2.502907875...\) (width scaling); critical exponents \(\nu, \eta, \beta\) related to eigenvalues of linearized RG operator; fractal dimension \(D = d - \beta/\nu\) for Ising class; anomalous dimension \(\gamma\) from fixed-point coupling. | CONNECTION: Feigenbaum's \(\alpha \approx 2.5029\) is near \(2.618\) (golden ratio squared \(\phi^2\)) and \(\delta \approx 4.669\) is close to \(4.618\) (\(\phi^3 + 1\)); period-doubling cascade ratio \(\delta\) 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