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

TL;DR

This paper extends high-temperature series for the spin-1/2 Ising model on simple cubic and body-centered cubic lattices to order β^{23}, providing refined estimates of critical parameters and universal amplitude ratios.

Contribution

The authors extended high-temperature series to order β^{23} for the Ising model on sc and bcc lattices, improving estimates of critical temperatures, exponents, and amplitude ratios.

Findings

Critical inverse temperatures: β_c^{sc}=0.221654(1), β_c^{bcc}=0.1573725(6)

Critical exponents: γ=1.2375(6), ν=0.6302(4)

Universal amplitude ratios: C_+/C_-=4.762(8), f_+/f_-=1.963(8)

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 $\beta^{sc}_c=0.221654(1)$ and $\beta^{bcc}_c=0.1573725(6)$. 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 $a^+_{\xi}/a^+_{\chi}=0.87(6)$.