Critical Temperatures of Ising Lattice Films

Ising lattices consisting of n=2, 3, 4, and 5 interacting plane square lattice layers are studied by hightemperature series expansions. Specifically, seven to nine terms of the zero-field susceptibility expansion have been obtained for (a) free-surface boundary conditions (in which each surface spin interacts with only five nearest neighbors) ; and (b) periodic boundary conditions (in which all spins interact equivalently with six nearest neighbors). Estimates of the critical temperatures T₂ (n) obtained by ratio and Pad\'e approximant techniques are presented. These results are consistent with the conjectures that T₂ () -T₂ (n) varies with thickness n, as n^- with =1 in case (a) and =1{₂}1. 56 in case (b) ; but other, somewhat larger, values of are not excluded.