  The physical origin of the backbendings in the equations of state of finite
but not necessarily small systems is studied in the Ising model with fixed
magnetization (IMFM) by means of the topological properties of the observable
distributions and the analysis of the largest cluster with increasing lattice
size. Looking at the convexity anomalies of the IMFM thermodynamic potential,
it is shown that the order of the transition at the thermodynamic limit can be
recognized in finite systems independently of the lattice size. General
statistical mechanics arguments and analytical calculations suggest that the
backbending in the caloric curve is a transient behaviour which should not
converge to a plateau in the thermodynamic limit, while the first order
transition is signalled by a discontinuity in other observables.
