Critical indices from perturbation analysis of the Callan-Symanzik equation

Recent results giving both the asymptotic behavior and the explicit values of the leading-order perturbation-expansion terms in fixed dimension for the coefficients of the Callan-Symanzik equation are analyzed by the the Borel-Leroy, Padé-approximant method for the n-component φ^4 model. Estimates of the critical exponents for these models are obtained for n=0, 1, 2, and 3 in three dimensions with a typical accuracy of a few one thousandths. In two dimensions less accurate results are obtained

Ising-Model Critical Indices in Three Dimensions from the Callan-Symanzik Equation

The coefficients in the Callan-Symanzik equations for a three-dimensional, continuous spin Ising model with an exp(-As^4+Bs^2) spin-weight factor are expanded in the dimensionless, renormalized coupling constant. These series are summed by the Padé-Borel method to yield the critical indices γ=1.241±0.002, η=0.02±0.02, ν=0.63±0.01, and Δ1=0.49±0.01