Two-Series Approach to Partial Differential Approximants: Three-Dimensional Ising Models

A two-series approach to partial differential approximant analysis of power series is presented. Instead of double series, f(x,y)=Σcᵢⱼxⁱyʲ, our approach uses two one-variable series in x, f and ∂f∂y, and has the efficiency and stability of one-variable methods. 21-term high-temperature series are analyzed for the susceptibility and correlation length squared for double-Gaussian Ising models on the bcc lattice. Critical exponents are γ=1.2378(6), 2ν=1.2623(6), and η=0.0375(5); correction-to-scaling exponents are θ_χ=0.52(3) and θ_ξ²=0.49(4); and the subdominant critical amplitude ratio is a_ξa_χ=0.83(5).