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
Year: 2026
Type: preprint
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 $ν\,$.
Source: arXiv (Cornell University)
Author: Liivand, Aleksandr
Institution: University of Tartu
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221806799