Mean-field theory for critical phenomena in bilayer systems

Magnetic systems consisting of a layer with finite thickness coupled to a semi-infinite bulk are studied with Ginzburg-Landau (GL) mean-field theory. The critical point of the system is determined in terms of the coefficients in the GL free-energy functional and the thickness of the thin layer. From the correlation functions within the semi-infinite bulk, an effective extrapolation length is able to be defined, although only the continuity of magnetization is assumed as the interfacial condition. This extrapolation length describes the coupling between the two subsystems and diverges with a new exponent ν=1. The critical behavior of spontaneous magnetization according to the variance of the layer thickness is derived as ms∼ L/Lc-1 with the critical thickness Lc and a new critical exponent βL=1/2.