Magnetic phase transitions in Heisenberg antiferromagnetic films with cubic lattices

Using the linked-cluster series expansions, high-temperature series for the free energy, and the staggered susceptibility of the spin-1 and spin- 3 2 Heisenberg antiferromagnetic model on the n -layers cubic lattice films are derived for n=2-7 layers. Series are obtained to seventh order for the simple-cubic lattice films and to sixth order for the body-centered-cubic lattice films with free-surface boundary conditions. The effects of finite size on critical-point behavior are studied by extrapolation of the high-temperature series. The shift in Néel temperature TN (n) for n -layers films is described by a finite-size scaling relation [TN (∞) - TN (n)] -TN (∞) that varies with thickness n, as n-λ for large n with a shift exponent λ, where TN (∞) is the bulk Neel temperature and λ is the inverse of the bulk correlation length exponent. Our results are qualitatively consistent with the predictions of finite-size scaling theory.