  We present the first detailed numerical study in three dimensions of a
first-order phase transition that remains first-order in the presence of
quenched disorder (specifically, the ferromagnetic/paramagnetic transition of
the site-diluted four states Potts model). A tricritical point, which lies
surprisingly near to the pure-system limit and is studied by means of
Finite-Size Scaling, separates the first-order and second-order parts of the
critical line. This investigation has been made possible by a new definition of
the disorder average that avoids the diverging-variance probability
distributions that plague the standard approach. Entropy, rather than free
energy, is the basic object in this approach that exploits a recently
introduced microcanonical Monte Carlo method.
