Ising model on the Sierpi ski gasket: thermodynamic limit versus infinitesimal field

Owing to extremely slow decay of correlations, the limit H → 0 presents a poor approximation for the Ising model on the Sierpi ski gasket. We present evidence of the competitive interplay between finite size scaling and thermodynamic scaling for this model, where both finite size and finite field induce an apparent phase transition. These observations may be relevant for the behavior of porous magnetic materials in real laboratory conditions