Monte Carlo study of thin magnetic Ashkin Teller films at the special point

The magnetic properties and critical behaviours of an Ashkin Teller spin-1/2 model magnetic thin-film systems are studied as part of the Monte Carlo simulation method, based on the Metropolis algorithm, in a simple cubic lattice. The effect of the interaction with the exchange coupling J(4) (surface and bulk) is studied. In addition, the phase diagrams present different ratios of the surface exchange interaction at the special point (R-s = J(2s)/J(2b))(sp), at which all the films thickness have the same critical temperature, these temperatures can be below, above or equal to the critical system bulk temperature. First and second order transitions appears in the system. Moreover, to the special point descriptions, we found another partially ordered phase at high temperature for certain values of the parameter's interaction. Finally, the effective surface exponents are computed.