Proof of the exact correlation-length exponent $\nu =\frac{\sqrt[3]{2}}{2}$ and algebraic relations for $\beta$ and $\gamma$ in the 3D Ising model

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 $\gamma$ and $\beta$. We proved that these expressions depend solely on the exact value of $\nu$.