text: The results obtained by MC simulations of the model 
  introduced in Sec. II will be presented starting from 
  n = 16, i.e. the highest investigated ﬁlm thickness which 
  still displays a bulk-like behaviour. 
  In Fig. 2 the spe- 
  ciﬁc heat for samples with n = 16 and lateral dimension 
  L = 24, 32, 48, 64 is shown. The location of the speciﬁc 
  heat maximum shows a quite deﬁnite evolution toward 
  the bulk transition temperature, T Ho 
  N ≃ 132 K10 (it is 
  worthwhile to note that for this XY model the mean ﬁeld 
  theory predicts a critical temperature T Ho 
  N,MF ≃ 198 K). 
  The intensity of the maximum of cv has been analyzed 
  by the MH technique for the same lateral dimensions (see 
  inset of Fig. 2): it clearly appears as it increases with L 
  in a smooth way. 
  
  z = 30.5◦). 
  The MC simulations outcomes for n = 16 we just pre- 
  sented appear quite diﬀerent with respect to those ob- 
  tained at the same thickness for the model with six cou- 
  pling constants along the z direction14,15. 
  Indeed, for 
  the J1-J2 model here investigated, we observe that all 
  layers order at the same temperature, and we do not ﬁnd 
  any hint of the block-phase, with inner disordered planes 
  intercalated to antiparallel quasi-FM four-layer blocks, 
  previously observed; sample MC runs we made using the 
  same hcp lattice employed in Refs. 14,15 shows that the 
  presence or absence of the block phase is not related to 
  the lattice geometry, but it is a consequence of the inter- 
  action range only. 