High-temperature critical properties of the Ising model on a triple of related lattices

Three regular three-dimensional lattices of coordination numbers, q = 3, 4, and 6 are introduced. Exact relations are derived among the specific-heat singularity amplitudes and among the susceptibility singularity amplitudes. Exact high-temperature series expansions for the partition function and the susceptibility are derived for the q = 3 and q = 6 lattices. Precise values of the critical temperature, susceptibility amplitude, critical energy, and critical entropy are obtained for all three lattices. The variation of Ising critical parameters with coordination number is discussed.