Extension to order β²³ of the high-temperature expansions for the spin-1/2 Ising model on simple cubic and body-centered cubic lattices

Using a renormalized linked-cluster-expansion method, we have extended to order β²³ the high-temperature series for the susceptibility χ and the second-moment correlation length ξ of the spin-1/2 Ising models on the sc and the bcc lattices. A study of these expansions yields updated direct estimates of universal parameters, such as exponents and amplitude ratios, which characterize the critical behavior of χ and ξ. Our best estimates for the inverse critical temperatures are β_c^sc=0.221654(1) and β_c^bcc=0.1573725(6). For the susceptibility exponent we get γ=1.2375(6) and for the correlation length exponent ν=0.6302(4). The ratio of the critical amplitudes of χ above and below the critical temperature is estimated to be C₊/C_-=4.762(8). The analogous ratio for ξ is estimated to be f₊/f_-=1.963(8). For the correction-to-scaling amplitude ratio we obtain a_ξ⁺/a_χ⁺=0.87(6).