A one-dimensional interacting particle system with a stochastic dynamics is
studied in the local mean field limit, extending the results of Lebowitz, Orlandi,
and Presutti to processes which satisfy detailed balance (with respect to Gibbs
measures). The behavior of the system below the critical temperature and inside
the unstable (spinodal) region is then investigated by means of computer
simulations. The experiments clearly indicate the presence of phase separation
and confirm the validity of some conjectures on the dynamics of the spinodal
decomposition.