  The equilibrium ensemble approach to disordered systems is used to
investigate the critical behaviour of the two dimensional Ising model in
presence of quenched random site dilution. The numerical transfer matrix
technique in semi- infinite strips of finite width, together with
phenomenological renormalization and conformal invariance, is particularly
suited to put the equilibrium ensemble approach to work. A new method to
extract with great precision the critical temperature of the model is proposed
and applied. A more systematic finite-size scaling analysis than in previous
numerical studies has been performed. A parallel investigation, along the lines
of the two main scenarios currently under discussion, namely the logarithmic
correction scenario (with critical exponents fixed in the Ising universality
class) versus the weak universality scenario (critical exponents varying with
the degree of disorder), is carried out. In interpreting our data, maximum care
is costantly taken to be open in both directions. A critical discussion shows
that, still, an unambiguous discrimination between the two scenarios is not
possible on the basis of the available finite-size data.
