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

Details 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 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

2000-06-06

arxiv.org/abs/hep-lat/0006009v3

Phys.Rev. B62 (2000) 14837-14843

Physics

High Energy Physics

High Energy Physics - Lattice

Misprints corrected, 8 pages, latex, no figures

Scientific paper

10.1103/PhysRevB.62.14837

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 $a^+_{\xi}/a^+_{\chi}=0.87(6)$.

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