text: As a ﬁnal issue we address the problem of the order 
  of the transitions observed at TN (n) and TC(n), respec- 
  tively. In particular, we focus our attention to the thick- 
  ness ranges where the chiral order parameter is relevant, 
  regions i) and ii) as deﬁned at the beginning of 
  i.e. 
  this Section. In Fig. 10 the equilibrium probability dis- 
  tribution of the energy for temperatures around TN (8) 
  (Fig. 10a) and TC(8) (Fig. 10b) is plotted: 
  for both 
  temperatures, no double peak structure is observed, so 
  that we have no direct indication for a ﬁrst order tran- 
  sition even if, according to precedent studies of Loison 
  and Diep17,18, the presence of a ﬁrst-order transition at 
  TN (n), cannot be completely excluded, as it could reveal 
  itself only when the lateral dimension L are much larger 
  than the largest correlation length. The same conclusion 
  about the order of transition is reached for any other in- 
  vestigated ﬁlm thickness, as the energy probability distri- 
  bution shape does not qualitatively change. This ﬁndings 
  agree with the results we got in previous MC simulations 
  discussed in Ref. 15, so that we may conclude that the 
  order of the observed transitions is not aﬀected by the 
  range of interactions. 