  Analytic phenomenological scaling is carried out for the random field Ising
model in general dimensions using a bar geometry. Domain wall configurations
and their decorated profiles and associated wandering and other exponents
$(\zeta,\gamma,\delta,\mu)$ are obtained by free energy minimization. Scaling
between different bar widths provides the renormalization group (RG)
transformation. Its consequences are (1) criticality at $h=T=0$ in $d \leq 2$
with correlation length $\xi(h,T)$ diverging like $\xi(h,0) \propto
h^{-2/(2-d)}$ for $d<2$ and $\xi(h,0) \propto \exp[1/(c_1\gamma h^{\gamma})]$
for $d=2$, where $c_1$ is a decoration constant; (2) criticality in $d =
2+\epsilon$ dimensions at $T=0$, $h^{\ast}= (\epsilon/2c_1)^{1/\gamma}$, where
$\xi \propto [(s-s^{\ast})/s]^{-2\epsilon/\gamma}$, $s \equiv h^{\gamma}$.
Finite temperature generalizations are outlined. Numerical transfer matrix
calculations and results from a ground state algorithm adapted for strips in
$d=2$ confirm the ingredients which provide the RG description.
