Criticality in diluted ferromagnets

We perform a detailed study of the critical behavior of the mean field diluted Ising ferromagnet using analytical and numerical tools. We obtain self-averaging for the magnetization and write down an expansion for the free energy close to the critical line. The scaling of the magnetization is also rigorously obtained and compared with extensive Monte Carlo simulations. We explain the transition from an ergodic region to a non-trivial phase by commutativity breaking of the infinite volume limit and a suitable vanishing field. We find full agreement among theory, simulations and previous results. © 2008 IOP Publishing Ltd