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PreprintCC BY-NC-ND 4.0arXiv

Proof of the exact correlation-length exponent ν= √[3]2/2 and algebraic relations for β and γ in the 3D Ising model

  • Aleksandr Liivand
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Abstract

Based on our previous results regarding critical exponent estimates for the 3D Ising model and scaling relations [1], we have proven that the exact value of the correlation-length exponent is √[3]2/2. This is in very close agreement with the most precise numerical estimates currently available. Using a group theoretical approach and some propositions of constructive geometry, we derived an exact construction of algebraic expressions for the critical exponents γ and β. We proved that these expressions depend solely on the exact value of ν.

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Cite

BibTeXRIS
BibTeX
@misc{liivand2026proof,
  title = {{Proof of the exact correlation-length exponent $ν= \frac\sqrt[3]22$ and algebraic relations for $β$ and $γ$ in the 3D Ising model}},
  author = {Aleksandr Liivand},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.17797},
  eprint = {2610.17797},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.17797},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Proof of the exact correlation-length exponent ν= √[3]2/2 and algebraic relations for β and γ in the 3D Ising model
AU  - Aleksandr Liivand
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.17797
UR  - https://arxiv.org/abs/2610.17797
AB  - Based on our previous results regarding critical exponent estimates for the 3D Ising model and scaling relations [1], we have proven that the exact value of the correlation-length exponent is √[3]2/2. This is in very close agreement with the most precise numerical estimates currently available. Using a group theoretical approach and some propositions of constructive geometry, we derived an exact construction of algebraic expressions for the critical exponents γ and β. We proved that these expressions depend solely on the exact value of ν.
ER  -