  We study the finite size corrections to the free energy density in disorder
spin systems on sparse random graphs, using both replica theory and cavity
method. We derive an analytical expressions for the $O(1/N)$ corrections in the
replica symmetric phase as a linear combination of the free energies of open
and closed chains. We perform a numerical check of the formulae on the Random
Field Ising Model at zero temperature, by computing finite size corrections to
the ground state energy density.
