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.
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