Finite-Size and Surface Effects in Heisenberg Films

High-temperature expansions for the zero-field susceptibility and specific heat to seventh order in K=JkBT are reported for ferromagnetic Heisenberg-model simple-cubic-lattice "films" of n=1, 2, , 6 layers. Extrapolation of the series yields reliable estimates of the susceptibility χ (and of the specific heats) down to temperatures at which T_χ30(T_χ)_T=∞. Firm conclusions about possible two-dimensional critical behavior cannot be reached, although the data are consistent with an exponent γ₂=3.0±0.5. The shifts of the apparent critical temperature Tc(n) from the $d=3$ bulk value can be described by a power law n^-λ with λ1.1±0.2. The surface susceptibility in the bulk limit diverges with an exponent γˣ=2.18±0.02 which appears to exceed the scaling prediction γˣ=γ₃+ν₃2.08; this could indicate the existence of a surface correlation length ξˣ(T) with exponent νˣ>ν₃.