  A one-dimensional Ising model with nearest neighbour interactions is applied
to study compaction processes in granular media. An equivalent particle-hole
picture is introduced, with the holes being associated to the domain walls of
the Ising model. Trying to mimic the experiments, a series of taps separated by
large enough waiting times, for which the system freely relaxes, is considered.
The free relaxation of the system corresponds to a T=0 dynamics which can be
analytically solved. There is an extensive number of metastable states,
characterized by all the holes being isolated. In the limit of weak tapping, an
effective dynamics connecting the metastable states is obtained. The steady
state of this dynamics is analyzed, and the probability distribution function
is shown to have the canonical form. Then, the stationary state is described by
Edwards thermodynamic granular theory. Spatial correlation functions in the
steady state are also studied.
