Effective scaling behavior of magnetization and Hamming distance in Ising thin films under a surface field

The recent improvements on the technology for developing high-quality thin magnetic films has renewed the interest in the study of surface effects in both static and dynamic magnetic responses. In this work, we use a Monte-Ca rlo algorithm with Metropolis dynamics together with a spreading of damage technique to study the interplay between the effects of finite thickness an d surface ordering field in thin ferromagnetic Ising (S = 1/2) films. We ca lculate, near the bulk critical temperature and several values of the surfa ce field, the dependence on the film thickness of the average magnetization M and Hamming distance D. We employ a finite size scaling analysis to show that both obey an effective one-parameter scaling but exhibit distinct cha racteristic surface fields. At their corresponding characteristic surface f ields both M and D become roughly thickness independent and we estimate the critical exponent characterizing the behavior of the typical scaling lengt hs.