Extension to order $β^{23}$ of the high-temperature expansions for the spin-1/2 Ising model on the simple-cubic and the body-centered-cubic lattices

Abstract

Using a renormalized linked-cluster-expansion method, we have extended to order $β^{23}$ 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 $β^{sc}_c=0.221654(1)$ and $β^{bcc}_c=0.1573725(6)$. For the susceptibility exponent we get $γ=1.2375(6)$ and for the correlation length exponent we get $ν=0.6302(4)$. 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 $a^+_ξ/a^+_χ=0.87(6)$.