Some results of high-temperature expansions for the ising model in an arbitrary magnetic field

Abstract

The high-temperature expansions of the function ϕ(χ,α), viz., the Legendre transform of the specific logarithm of the statsum of the Ising model in an arbitrary external field, are investigated. The computed surface of the thermodynamic potential ϕ is well described by the scaling form of the similarity hypothesis. For lattices with second-neighbor interaction the calculations clearly indicate the weak nonuniversality of the critical behavior (the index γ for the fcc-2 and sc-2 lattices with coordination number q=18 is closer to the value 1.21 than to the standard value 1.25). It is noted that the bcc-2 lattice has a universal behavior, i.e., nonuniversality is observed for lattices with coordination number q⩾18. High-temperature series in temperature-magnetization variables are presented in the Appendix for three-space lattices with both first-neighbor as well as second-neighbor interactions, to within the ninth and the eighth orders, respectively.