  We consider geometrical clusters (i.e. domains of parallel spins) in the
square lattice random field Ising model by varying the strength of the Gaussian
random field, $\Delta$. In agreement with the conclusion of previous
investigation (Phys. Rev. E{\bf 63}, 066109 (2001)), the geometrical
correlation length, i.e. the average size of the clusters, $\xi$, is finite for
$\Delta > \Delta_c \approx 1.65$ and divergent for $\Delta \le \Delta_c$. The
scaling function of the distribution of the mass of the clusters as well as the
geometrical correlation function are found to involve the scaling exponents of
critical percolation. On the other hand the divergence of the correlation
length, $\xi(\Delta) \sim (\Delta - \Delta_c)^{-\nu}$, with $\nu \approx 2.$ is
related to that of tricritical percolation. It is verified numerically that
critical geometrical correlations transform conformally.
