  We present analytical results for the strongly anisotropic random field Ising
model, consisting of weakly interacting spin chains. We combine the mean-field
treatment of interchain interactions with an analytical calculation of the
average chain free energy (``chain mean-field'' approach). The free energy is
found using a mapping on a Brownian motion model. We calculate the order
parameter and give expressions for the critical random magnetic field strength
below which the ground state exhibits long range order and for the critical
temperature as a function of the random magnetic field strength. In the limit
of vanishing interchain interactions, we obtain corrections to the
zero-temperature estimate by Imry and Ma [Phys. Rev. Lett. 35, 1399 (1975)] of
the ground state density of domain walls (spin-flips) in the one-dimensional
random field Ising model. One of the problems to which our model has direct
relevance is the lattice dimerization in disordered quasi-one-dimensional
Peierls materials, such as the conjugated polymer trans-polyacetylene.
