Owing to extremely slow decay of correlations, the limit H --> 0 prese
nts a poor approximation for the Ising model on the Sierpinski gasket.
We present evidence of the competitive interplay between finite size
scaling and thermodynamic scaling for this model, where both finite si
ze and finite field induce an apparent phase transition, These observa
tions may be relevant for the behavior of porous magnetic materials in
real laboratory conditions.