1 Finite-size scaling study of the d = 4 site-diluted Ising model ∗.

If a pure system has a specific heat exponent α > 0 the Universality Class changes when the dilution is introduced in the model (Harris criterion [1]), while it remains unchanged if α < 0 (i.e. the Universality Class is that of the pure model). In the Ising model in 4 (or 2) dimensions α = 0 and the Harris criterion does not apply. Perturbative renormalization group (PRG) computations for d = 4 predict Mean Field with Logarithmic Corrections. On the other hand, previous Monte Carlo (MC) results pointed to non Mean Field behavior [2]. In d = 2 there are also MC studies that conclude a change of the Universality Class. We describe here the results of a higher statistics MC study [3]. A Finite-Size Scaling (FSS) approach has been used in order to study large lattices in the critical region. Results on the d = 2 case are also briefly described [4].