The Prime-Fractal Renormalization Group in the Universal Model Framework: A Universal Framework for Critical Phenomena from Number Theory to Quantum Many-Body Systems
Year: 2025
Type: article
Abstract: We introduce the Prime-Fractal Renormalization Group (PFRG), a comprehensive theoretical framework leveraging discrete prime-fractal self-similarity to describe critical phenomena across all scales of physics. By implementing prime-modulated blocking transformations, we derive beta functions with number-theoretic oscillations and identify novel universality classes exhibiting anomalous scaling dimensions. Monte Carlo simulations on Prime-Sierpiński lattices validate predicted critical exponents (ν = 2.0 ± 0.1, η = 1.0 ± 0.1) for 2D/3D Ising and O(2) models, demonstrating universality beyond scalar field theory. SU(2) gauge theory calculations on 8³ lattices with prime-weighted actions reveal modified asymptotic freedom and β-function corrections. Null-model Monte Carlo with randomized prime masks confirms that observed scaling requires genuine arithmetic structure, not generic disorder. We establish mathematical foundations through convergence proofs, continuum limit existence, and fixed point uniqueness, extending the framework to quantum many-body systems, consciousness models, and tensor network algorithms. Experimental proposals include cold atom setups with comprehensive error analysis. The framework predicts observable prime-number resonances in correlation functions and establishes deep connections between discrete number-theoretic structure and continuous physical laws, opening new directions for both fundamental physics and applied quantum technologies This project was developed by Marco Gericke, with structured assistance from a large language model. All scientific concepts and conclusions were generated, verified, and interpreted by the author. Dedicated to Peter Plichta, who envisioned the code before it could be computed.
Author: Gericke, Marco
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6950158166
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