  The damage spreading method (DS) provided a useful tool to obtain analytical
results of the thermodynamics and stability of the 2D Ising model --amongst
many others--, but it suffered both from ambiguities in its results and from
large computational costs. In this paper we propose an alternative method, the
so called self-overlap method, based on the study of correlation functions
measured at subsequent time steps as the system evolves towards its
equilibrium. Applying markovian and mean field approximations to a 2D Ising
system we obtain both analytical and numerical results on the thermodynamics
that agree with the expected behavior. We also provide some analytical results
on the stability of the system. Since only a single replica of the system needs
to be studied, this method would seem to be free from the ambiguities that
afflicted DS. It also seems to be numerically more efficient and analytically
simpler.
