New rigorous inequality for critical exponents in the Ising model

Abstract

Defining the correlation length by the $\phi \mathrm{th}$ moment of the magnetization-magnetization correlation, we give a simple proof of the inequality $\phi \nu \left(\phi \right)>\mathrm{}2\mathrm{}{\Delta }_4-\gamma (\phi >d)$ for the ferromagnetic Ising model in $d$ dimensions. We briefly discuss the relevance of this inequality for the constructive ${\phi }_d^4$ approach.