Monte Carlo study of randomly diluted ferromagnetic thin films

Using Monte Carlo simulations, we have studied the Ising model with random, nonmagnetic impurities on an N×N×L simple cubic lattice. Systems with ferromagnetic nearest-neighbor coupling and periodic boundary conditions in the x-y plane are studied for N=40 and 1≤L≤40 for several values of p, the concentration of magnetic ions. The average magnetization, susceptibility, and specific heat are calculated as a function of temperature for different values of L and p. The transition temperature $T_c$ decreases monotically to zero as the concentration p decreases towards the percolation threshold for the width L. The shift of $T_c$ is consistent with $L^{\mathrm{-}\lambda }$, where λ is equal to 1.56 in the critical region.