New relation for critical exponents in the Ising model

The Ising model in a transverse field is considered at T=0T=0. From the analysis of the power low behaviors of the energy gap and the order parameter as functions of the field a new relation between the respective critical exponents, β⩾1/(8s2)β⩾1/(8s2), is derived. By using the Suzuki equivalence from this inequality a new relation for critical exponents in the Ising model, β⩾1/(8ν2)β⩾1/(8ν2), is obtained. A number of numerical examples for different cases illustrates the generality and validity of the relation. By applying this relation the estimation ν=(1/4)1/3≈0.62996ν=(1/4)1/3≈0.62996 for the 3D-Ising model is proposed.