Critical Point of Magnetic Films on the Ising Model

D. L. Lin ； Jing-Tian Ou

《Chinese Journal of Physics》 32卷5S期 (1994/10) Pp. 703-714

並列摘要

In this article, we review a new theory proposed recently for the treatment of the critical point of film structures of spin systems on the Ising model. Based on the variational cumulant expansion of the free energy, the theory provides for the first time a way of analytical calculations of the critical point T, for Ising films of arbitrary thickness. The method is capable to treat inhomogeneous Ising spin systems of various lattice structures with different geometry. For the purpose of illustration, we first review the theory and some of our previous results for systems with nearestneighbor interaction and isotropic coupling. Then we extend our calculation to include the next-nearest-neighbor interactions, and to treat nearest neighbor interactions with anisotropic coupling. In every case, Tc(L) is found for simple cubic, body-centered cubic and face-centered cubic lattices, where L denotes the number of spin layers in the film. Other considerations such as the inhomogeneity of the coupling strength and the interface effects are also discussed briefly.