A transfer matrix study of layering transitions in Ising model thin films

Overview & Synopsis

We study the layering transitions for a spin 1/2 Ising model under uniform and variable magnetic field in a film of finite thickness limited by a single substrate. Using finite size transfer matrix and mean field theory, we show that the layering transitions occurs only at a temperature higher than TL. The latter depends on the nature of the surface field hs, and on its strength Hs, In the case where the surface field is short-range, the transfer matrix predicts a splitting of a single multi-layer transition into several single-layer transitions whereas mean field theory does not.