  The Ising model in the presence of a random field is investigated within the
mean field approximation based on Landau expansion. The random field is drawn
from the trimodal probability distribution $P(h_{i})=p \delta(h_{i}-h_{0}) + q
\delta (h_{i}+h_{0}) + r \delta(h_{i})$, where the probabilities $p, q, r$ take
on values within the interval $[0,1]$ consistent with the constraint $p+q+r=1$
(asymmetric distribution), $h_{i}$ is the random field variable and $h_{0}$ the
respective strength. This probability distribution is an extension of the
bimodal one allowing for the existence in the lattice of non magnetic particles
or vacant sites. The current random field Ising system displays second order
phase transitions, which, for some values of $p, q$ and $h_{0}$, are followed
by first order phase transitions, thus confirming the existence of a
tricritical point and in some cases two tricritical points. Also, reentrance
can be seen for appropriate ranges of the aforementioned variables. Using the
variational principle, we determine the equilibrium equation for magnetization,
solve it for both transitions and at the tricritical point in order to
determine the magnetization profile with respect to $h_{0}$.
