The thermodynamic properties of a magnetically coupled two-layer system using the shift operator matrix method
Abstract
In the present research, the Shift Operator Matrix (SOM) method is extended to a three dimensional, 2 × M × ∞ cubic-cell Ising model. Different kinds of spin particles are located on this lattice. Particles of one type are located in the upper layer while particles of the second type are located in the lower layer. In an attempt to simulate the recent SMOKE experiments and theoretical Monte Carlo simulations, the upper layer is not fully occupied (the coverage varies from 0 to 1), while the lower layer is fully occupied. An exact numerical method (without the use of numerical approximations to calculate derivatives) is used to evaluate thermodynamic quantities such as the coverage, magnetization, and heat capacity. Different adjustable parameters enable us to discuss and analyze the thermodynamic properties of a two-layer system and their dependence on such factors as spin-spin coupling. By proper choice of the model's parameters the system can be reduced to a classical two-dimensional Ising model, which can be used for computational comparison. Results of considering 25 different parameter combinations show that there are eight cases whose Curie temperature vs. thickness relationship better fit the experimental SMOKE results than do the Monte Carlo simulations. The heat capacity and magnetization of this two-layer system are discussed and analyzed for various parameter choices and are shown to be consistent with real physical systems. It is shown that the two-layer system also possesses a critical reduced chemical potential. The dependence of this critical chemical potential on system parameters is also investigated.
This paper has been withdrawn.