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arXiv · 2610.17797

Proof of the exact correlation-length exponent $ν= \frac{\sqrt[3]{2}}{2}$ 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 $\frac{\sqrt[3]{2}}{2}$. 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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Aleksandr Liivand. 2026-10-13. Proof of the exact correlation-length exponent $ν= \frac{\sqrt[3]{2}}{2}$ and algebraic relations for $β$ and $γ$ in the 3D Ising model. https://arxiv.org/abs/2610.17797

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