text: In the following we will denote with n the ﬁlm thick- 
  ness, i.e. the number of spin layers along the z direction, 
  and with L×L the number of spins in each layer (i.e., L 
  is the lattice size along both the x and y directions). In 
  our simulations thickness values from 1 to 24 were con- 
  sidered, while the range of lateral size L was from 8 to 
  64. Periodic boundary conditions were applied along x 
  and y, while free boundaries were obviously taken along 
  the ﬁlm growth direction z. 
  
  Thermal equilibrium was attained by the usual 
  Metropolis algorithm19, 
  supplemented by the over- 
  relaxed technique20 in order to speed-up the sampling 
  of the spin conﬁguration space: a typical “Monte Carlo 
  step” was composed by four Metropolis and four-ﬁve 
  over-relaxed moves per particle. Such judicious mix of 
  moves is able both to get faster the thermal equilibrium 
  and to minimize the correlation “time” between succes- 
  sive samples, i.e. the undesired eﬀects due to lack of in- 