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PreprintCC BY 4.0Zenodo

Topological Phase Transitions Beyond Landau's Symmetry-Breaking Paradigm — E8 Intelligence Research

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

FINDING: Topological phase transitions evade Landau's symmetry-breaking paradigm, with deconfined quantum criticality and non-Abelian transitions in 3+1D as concrete examples. | MATH: Landau free energy F = F0 + a(T−Tc)ϕ2 + bϕ4 fails when order parameter ϕ is ill-defined; topological invariants (e.g., Chern number C = 1/2π∫B Fxy d2k, or winding number W = 1/24π2∫ Tr(g−1dg)3) replace local order parameters. Deconfined quantum criticality: fractionalized excitations (spinons) with gauge field aμ, critical exponents not from Landau-Ginzburg-Wilson. | CONNECTION: Topological order links to modular tensor categories (fusion rules Nabc, braiding Rab, F-matrices) — these encode non-commutative geometry, echoing root-system Weyl groups (e.g., A2 hexagonal lattice, D4 tetrahedral symmetry) but in momentum space. No direct 0.382/0.618/1.618 ratios appear in the cited abstracts;

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{caldin2026topological,
  title = {{Topological Phase Transitions Beyond Landau's Symmetry-Breaking Paradigm — E8 Intelligence Research}},
  author = {Andrew Stewart Caldin},
  howpublished = {Zenodo},
  year = {2026},
  month = oct,
  doi = {10.5281/zenodo.23587051},
  url = {https://zenodo.org/records/23587051},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Topological Phase Transitions Beyond Landau's Symmetry-Breaking Paradigm — E8 Intelligence Research
AU  - Andrew Stewart Caldin
PY  - 2026
DA  - 2026/10/23
PB  - Zenodo
DO  - 10.5281/zenodo.23587051
UR  - https://zenodo.org/records/23587051
AB  - FINDING: Topological phase transitions evade Landau's symmetry-breaking paradigm, with deconfined quantum criticality and non-Abelian transitions in 3+1D as concrete examples. | MATH: Landau free energy F = F_0 + a(T−T_c)ϕ^2 + bϕ^4 fails when order parameter ϕ is ill-defined; topological invariants (e.g., Chern number C = 1/2π∫_B F_xy d^2k, or winding number W = 1/24π^2∫ Tr(g^−1dg)^3) replace local order parameters. Deconfined quantum criticality: fractionalized excitations (spinons) with gauge field a_μ, critical exponents not from Landau-Ginzburg-Wilson. | CONNECTION: Topological order links to modular tensor categories (fusion rules N_ab^c, braiding R_ab, F-matrices) — these encode non-commutative geometry, echoing root-system Weyl groups (e.g., A_2 hexagonal lattice, D_4 tetrahedral symmetry) but in momentum space. No direct 0.382/0.618/1.618 ratios appear in the cited abstracts;  Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER  -