Antiferromagnetic Susceptibility of the Plane Triangular Ising Lattice

Abstract

The magnetic moment transformation developed by Fisher enables the antiferromagnetic susceptibility of the plane triangular Ising lattice to be expanded as a power series that converges over the whole temperature range $0<~T<~\infty$. The dominant asymptotic behavior of the coefficients conjectured from extrapolations by Domb and Sykes, and independently by Park, has been established theoretically by Fisher. A counting theorem based on the method of Oguchi enables the first twelve terms of the expansion to be derived. It is found possible to evaluate the susceptibility numerically over the whole temperature range with a maximum error of 0.1% at $T=0\mathrm{}$. It is concluded that the specific susceptibility per spin ($\frac{\mathrm{kT}{\chi }_0}{m^2}$) falls smoothly from unity at $T=\infty$ to a value at $T=0\mathrm{}$ which does not differ by more than 0.1% from $\frac{5}{36}$, and the form of the counting theorem leads it to be surmised that it is exactly $\frac{5}{36}$.