Extension to order ${\beta }^{23}$ 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 ${\beta }^{23}$ the high-temperature series for the susceptibility $\chi$ and the second-moment correlation length $\xi$ 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 $\chi$ and $\xi$. Our best estimates for the inverse critical temperatures are ${\beta }_c^{sc}=0.221654(1)$ and ${\beta }_c^{bcc}=0.1573725(6)$. For the susceptibility exponent we get $\gamma =1.2375(6)$ and for the correlation length exponent we get $\nu =0.6302(4)$. The ratio of the critical amplitudes of $\chi$ above and below the critical temperature is estimated to be $C_{+}/C_{-}=4.762(8)$. The analogous ratio for $\xi$ is estimated to be $f_{+}/f_{-}=1.963(8)$. For the correction-to-scaling amplitude ratio we obtain $a_{\xi }^{+}/a_{\chi }^{+}=0.87(6)$.

Comments: Misprints corrected, 8 pages, latex, no figures