Using the linked-cluster series expansions, high-temperature series for the free energy, and the staggered susceptibility of the spin-1 and spin-$\frac{3}{2}$ 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 $T_N\left(n\right)$ for $n$-layers films is described by a finite-size scaling relation $[T_N\left(\infty \right)-T_N\left(n\right)]∕T_N\left(\infty \right)$ that varies with thickness $n$, as $n^{-\lambda }$ for large $n$ with a shift exponent $\lambda$, where $T_N\left(\infty \right)$ is the bulk Neel temperature and $\lambda$ is the inverse of the bulk correlation length exponent. Our results are qualitatively consistent with the predictions of finite-size scaling theory.

• Received 15 September 2004

DOI:https://doi.org/10.1103/PhysRevB.71.134524