Convergent Discovery of Critical Phenomena Mathematics Across Disciplines
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866908895542247424 |
|---|---|
| author | Stephenson, Bruce Macomber, Robin |
| author_facet | Stephenson, Bruce Macomber, Robin |
| contents | Techniques for detecting critical phenomena -- phase transitions where correlation length diverges and small perturbations have large effects -- have been developed across multiple fields over nine decades. We survey between six and twelve disciplines (depending on classification criteria) where researchers derived functionally corresponding measures of correlation scaling, with little documented awareness of each other's work. The physicist's correlation length $ξ$, the cardiologist's DFA scaling exponent $α$, the financial analyst's Hurst exponent $H$, and the machine learning engineer's spectral radius $χ$ all detect critical signatures under different notation.
We classify each surveyed domain as independent derivation, domain transfer, or empirical precursor, and present citation network evidence that cross-domain citations remained significantly below random-mixing expectations (under a simple null model of domain mixing) during the formative period (1987--2010). The framework that motivated this investigation -- derived from distributed systems engineering and presented in the Supplementary Material -- is excluded from the survey count given the authors' dual role.
Building on prior syntheses -- notably Sornette's 2004 textbook -- this paper contributes a taxonomy of discovery types and quantitative documentation of the convergence pattern. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_22389 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Convergent Discovery of Critical Phenomena Mathematics Across Disciplines Stephenson, Bruce Macomber, Robin Physics and Society Statistical Mechanics 82B26, 82B27 Techniques for detecting critical phenomena -- phase transitions where correlation length diverges and small perturbations have large effects -- have been developed across multiple fields over nine decades. We survey between six and twelve disciplines (depending on classification criteria) where researchers derived functionally corresponding measures of correlation scaling, with little documented awareness of each other's work. The physicist's correlation length $ξ$, the cardiologist's DFA scaling exponent $α$, the financial analyst's Hurst exponent $H$, and the machine learning engineer's spectral radius $χ$ all detect critical signatures under different notation. We classify each surveyed domain as independent derivation, domain transfer, or empirical precursor, and present citation network evidence that cross-domain citations remained significantly below random-mixing expectations (under a simple null model of domain mixing) during the formative period (1987--2010). The framework that motivated this investigation -- derived from distributed systems engineering and presented in the Supplementary Material -- is excluded from the survey count given the authors' dual role. Building on prior syntheses -- notably Sornette's 2004 textbook -- this paper contributes a taxonomy of discovery types and quantitative documentation of the convergence pattern. |
| title | Convergent Discovery of Critical Phenomena Mathematics Across Disciplines |
| topic | Physics and Society Statistical Mechanics 82B26, 82B27 |
| url | https://arxiv.org/abs/2601.22389 |