Magnetic behaviour of Ising multilayers

The magnetic behavior of Ising multilayer system including nearest neighbor and next nearest neighbor interactions is investigated by use of variational cumulant expansion (VCE) method. The formulae for spontaneous magnetization, coercivity, Curie point, Neel point, susceptbility and molecular field parameters responding to the number of layers are deduced and discussed numerically. It is exactly demonstrated that, in 2-dimensional and 3-dimensional systems, the spontaneous magnetization calculated by first order of the VCE is the same as the results of mean field theory. This means that the first order of VCE is valid in low temperature. The validity of VCE in high temperature (above the critical point) is explained by the physical meaning of VCE method.