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

Abstract

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 α, β, and γ can be determined. The values are in general agreement with those found by Pade analysis. A critique of the accuracy of the method and its possibilities is given.