ABSTRACT
In this chapter, the author shows the critical behavior of magnetic thin films as a function of the film thickness. He uses the ferromagnetic Ising model with the high-resolution multiple histogram Monte Carlo (MC) simulation. The author shows that though the 2D behavior remains dominant at small thicknesses, there is systematic continuous deviation of the critical exponents from their 2D values. He explains these deviations using the concept of “effective” exponents suggested by Capehart and Fisher in a finite-size analysis. Low-lying energy modes contribute to reduce in general surface magnetization at finite temperatures. One of consequences is the surface disordering which may occur at a temperature lower than that for interior magnetization. If the thickness is larger than the correlation length at the transition, than the first-order transition should remain. On the other hand, if the thickness is smaller than that correlation length, the spins then feel an “infinite” correlation length across the film thickness resulting in a second-order transition.
