Partial Test of the Universality Hypothesis: The Case of Different Coupling Strengths in Different Lattice Directions

High-temperature series expansions are used to examine the dependence of critical-point exponents upon lattice anisotropy (different interaction strengths in different directions in the lattice). The two-spin correlation function C₂ (r) is calculated to tenth order in (1{k₁T}) for the Ising Hamiltonian H₋ ₀₍₈ₒ=-Jₗₘ〈ij〉S₈^zS₉^z-Jₙ〈ij〉S₈^zS₉^z for a wide range of anisotropy parameters RJₙ{Jₗₘ} and for both the sc and fcc lattices; here the first summation is over all pairs of nearest-neighbor sites whose relative displacement vector {r}₈₉ has no z component, while the second summation is over all other pairs of nearest-neighbor sites. Hence for R=0, both the sc and fcc lattices reduce to the two-dimensional square lattice, while in the limit R, the sc becomes a one-dimensional linear chain and the fcc becomes two noninteracting three-dimensional bcc lattices. The series for C₂ (r) are then used to obtain series of corresponding lengths for the specific heat, susceptibility, and second moment. Analysis of these series yields results consistent with the universality hypothesis of critical-point exponents. Specifically, it is found that when lattice anisotrophy is introduced, the critical-point exponents studied (the susceptibility exponent and the correlation length exponent) do not appear to change from their values for an isotropic lattice. The problem of next-nearest-neighbor interactions is treated using similar methods in Paper II of this series (and briefly discussed in this paper).