eng Science and Education Publishing International Journal of Physics 2333-4576 2018-07-27 6 4 116 121 10.12691/ijp-6-4-3 IJP2018643 article A. Waddahou 1 M. Chahid mustapha.chahid@gmail.com 1 A. Maarouf 1 F. Benzouine 1 Polymer Physics and Critical Phenomena Laboratory, Faculty of Sciences Ben M'sik, Hassan II University of Casablanca, P. O. Box 7955, Casablanca, Morocco The purpose of this work is the investigation of the critical surface effects of two strongly coupled paramagnetic sublattices exhibiting a para-ferrimagnetic transition. The model is of Landau-Ginzburg type, whose bulk free energy is a functional of two kind of order parameters (local magnetizations) and This free energy involves, beside quadratic and quartic terms in both and , a lowest-order coupling, where Co<0 is the coupling constant measuring the interaction between the two sublattices. Two terms H and are also introduced, to describe the interaction within an external magnetic field H. We introduce a surface free energy expanded in terms of the local order parameters. The magnetization at the surface are s and We show, in particular, that the model can be reduced to an effective theory written in terms of the overall magnetization and the associated fraction of magnetization . This formulation leads us to define an effective extrapolation length s. We then derive all the critical properties of the system close to the critical temperature Tc. In particular, we determine the critical behavior of the overall surface magnetization , in terms of b above and below Tc. The variations of s with the magnetic field H, and when a surface field Hs is applied actually at Tc, are derived. We determine, also, the associated susceptibilities at the surface s and s.s. The determination of the full profile of the magnetization close to the surface will be the subject of a future communication. http://pubs.sciepub.com/ijp/6/4/3/ijp-6-4-3.pdf sublattices coupling paramagetism ferrimagnetism transition critical surface effects