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PreprintCC BY 4.0Zenodo

Entropy Production Barrier Governs Disorder-Driven Phase Transitions in Random-Anisotropy XY Ferromagnets — E8 Intelligence Research

  • Andrew Stewart Caldin1
  1. 1Independent Researcher, United Kingdom
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Abstract

FINDING: The Clausius-Duhem inequality (CDI) is the local, continuum form of the second law, imposing a monotonicity constraint on entropy production that acts as a topological barrier to phase transitions; the XY ferromagnet with random anisotropy exhibits disorder-driven phase transitions whose critical behavior is governed by the competition between continuous symmetry and quenched randomness. | MATH: CDI: ρ η̇ + ∇ · (q/T) − ρ r/T ≥ 0, equivalently η̇ ≥ −∇ · (q/T) + ρ r/T. In terms of Helmholtz free energy ψ = e − Tη: −ρ(ψ̇ + η Ṫ) + σ:D − (q·∇ T)/T ≥ 0. For the XY model: Hamiltonian H = −J ∑⟨ ij⟩ Si · Sj − ∑i Di (n̂i · Si)2, with random anisotropy axes n̂i. Order parameter M = ⟨ |∑i Si|/N ⟩; susceptibilit

Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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Cite

BibTeXRIS
BibTeX
@misc{caldin2026entropy,
  title = {{Entropy Production Barrier Governs Disorder-Driven Phase Transitions in Random-Anisotropy XY Ferromagnets — E8 Intelligence Research}},
  author = {Andrew Stewart Caldin},
  howpublished = {Zenodo},
  year = {2026},
  month = oct,
  doi = {10.5281/zenodo.23431098},
  url = {https://zenodo.org/records/23431098},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Entropy Production Barrier Governs Disorder-Driven Phase Transitions in Random-Anisotropy XY Ferromagnets — E8 Intelligence Research
AU  - Andrew Stewart Caldin
PY  - 2026
DA  - 2026/10/17
PB  - Zenodo
DO  - 10.5281/zenodo.23431098
UR  - https://zenodo.org/records/23431098
AB  - FINDING: The Clausius-Duhem inequality (CDI) is the local, continuum form of the second law, imposing a monotonicity constraint on entropy production that acts as a topological barrier to phase transitions; the XY ferromagnet with random anisotropy exhibits disorder-driven phase transitions whose critical behavior is governed by the competition between continuous symmetry and quenched randomness. | MATH: CDI: ρ η̇ + ∇ · (q/T) − ρ r/T ≥ 0, equivalently η̇ ≥ −∇ · (q/T) + ρ r/T. In terms of Helmholtz free energy ψ = e − Tη: −ρ(ψ̇ + η Ṫ) + σ:D − (q·∇ T)/T ≥ 0. For the XY model: Hamiltonian H = −J ∑_⟨ ij⟩ S_i · S_j − ∑_i D_i (n̂_i · S_i)^2, with random anisotropy axes n̂_i. Order parameter M = ⟨ |∑_i S_i|/N ⟩; susceptibilit  Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER  -