  We have studied the one dimensional Dyson hierarchical model in presence of a
random field. This is a long range model where the interactions scale with the
distance with a power law-like form J(r) ~ r^{-\rho} and we can explore mean
field and non-mean field behavior by changing \rho. Thus, it can be used to
approach the phase transitions in finite-dimensional disordered models. We
studied the model at T=0 and we numerically computed its critical exponents in
the non-mean field region for Gaussian disorder. We then computed an analytic
expression for the critical exponent \delta, that holds in the non-mean field
region, and we noted an interesting relation between the critical exponents of
the disordered model and the ones of the pure model, that seems to break down
in the non-mean field region. We finally compare our results for the critical
exponents with the expected ones in D-dimensional short range models and with
the ones of the straightforward one dimensional long range model.
