Surface critical behavior of thin Ising films at the ‘special point’

The critical surface phenomena of a magnetic thin Ising film is studied using numerical Monte-Carlo method based on Wolff cluster algorithm. With varying the surface coupling, js=Js/J, the phase diagram exhibits a special surface coupling jsp at which all the films have a unique critical temperature Tc for an arbitrary thickness n. In spite of this, the critical exponent of the surface magnetization at the special point is found to increase with n. Moreover, non-universal features as well as dimensionality crossover from two- to three-dimensional behavior are found at this point.