Phase transition of the fcc multilayer films with nearest neighbor and next-nearest neighbor interactions

Based on Monte Carlo simulation, the magnetic properties of the Heisenberg face-centered cubic (fcc) multilayer films with competitive nearest neighbor (NN) and next-nearest neighbor (NNN) interactions are investigated. Four different kinds of magnetic phases and spin orderings depending on the relative signs and strengths of NN and NNN interactions are presented and discussed. A new 4×4 transfer matrix method which is used to calculate the phase transition of films with NN and NNN interactions is derived. In addition, different order parameters are constructed to characterize the transition in different systems, and a complete description of phase diagram displaying transitions between those various phases is also reported. Finally, it is found that the simulated results are consistent with those derived by 4×4 transfer matrix method.