“…Numerous theoretical techniques have been used to examine the magnetic characteristics of semi-infinite systems to explain the phenomena seen in experiments. Mean-field approximation (MFA) [10,11], Monte Carlo simulation (MCS) [12,13], renormalization group theory (RGT) [14,15], effective-field theory (EFT) [16], finite cluster approximation [17], Landau theory [18], and series expansions [19] have all been used to investigate the spin- 1 2 semi-infinite Ising model. Most of these works describe four different forms of second-order phase transitions based on the ratio R = J B /J S of bulk and surface interactions: ordinary, extraordinary, surface, and special phase transitions.…”