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 Tc(n) obtained by ratio and Pad\'e approximant techniques are presented. These results are consistent with the conjectures that Tc(∞)-Tc(n) varies with thickness n, as n^-λ with λ=1 in case (a) and λ=1νc1.56 in case (b); but other, somewhat larger, values of λ are not excluded.