Abstract: | The lattice Green's function for the simple cubic lattice (γ = 1) and tetragonal lattice at an arbitrary point (l, m, n) is evaluated, assuming a ? 0, γ ? 0 without loss of generality. The integral I(a; l, m, n; γ) which has singularities at a = ± γ ± 1 ± 1, is expressed in all regions of (a, γ), i.e., for (i) a > 2 + γ, (ii) 2 ? γ > a > γ(γ < 2), (iii) a <γ ? 2 (γ > 2), (iv) a < 2 ? γ (1 < γ < 2) and γ > a (0 < γ < 1), (v) |a ? γ| < 2 and a + γ > 2, in terms of Kampé de Fériet function by the method of the analytic continuation using the Mellin-Barnes type integral. The numerical values are shown in figures. The high temperature susceptibilities of the Heisenberg model of the ferro- and antiferromagnets are calculated using the results of I(a; l, m, n; γ), showing a shift from three to two dimensions and that from three to one dimensions. The correlation function of the isotropic ferromagnet is calculated and the critical index ν is observed to be 1. |