Critical field and low-temperature critical indices of the ferromagnetic Ising model

For the ferromagnetic Ising model the low-temperature series expansion with temperature grouping polynomials is studied. We show that certain roots of these polynomials converge to the critical field $H_c$, and in favorable cases we can determine the critical field quite accurately. Knowing the critical field $H_c$, one can determine the asymptotic behavior of the temperature grouping polynomials numerically. The essential feature is a power-law behavior. Hence, the low-temperature critical indices ${\alpha }^{\prime }$, $\beta$, and ${\gamma }^{\prime }$ can be determined. The values are in general agreement with those found by Padé analysis. A critique of the accuracy of the method and its possibilities is given.