Critical behavior of magnetic thin films as a function of thickness

We study the critical behavior of magnetic thin films as a function of the film thickness. We use the ferromagnetic Ising model with the high-resolution multiple histogram Monte Carlo (MC) simulation. We show that though the 2D behavior remains dominant at small thicknesses, there is a systematic continuous deviation of the critical exponents from their 2D values. We observe that in the same range of varying thickness the deviation of the exponent $\nu$ is rather small, while exponent $\beta$ suffers a larger deviation. We explain these deviations using the concept of "effective" exponents suggested by Capehart and Fisher in a finite-size analysis. The shift of the critical temperature with the film thickness obtained here by MC simulation is in an excellent agreement with their prediction.