  We study numerically the zero temperature Random Field Ising Model on cubic
lattices of various linear sizes $L$ in three dimensions. For each random field
configuration we vary the ferromagnetic coupling strength $J$. We find that in
the infinite volume limit the magnetization is discontinuous in $J$. The energy
and its first $J$ derivative are continuous. The approch to the thermodynamic
limit is slow, behaving like $L^{-p}$ with $p \sim .8$ for the gaussian
distribution of the random field. We also study the bimodal distribution $h_{i}
= \pm h$, and we find similar results for the magnetization but with a
different value of the exponent $p \sim .6 $. This raises the question of the
validity of universality for the random field problem.
