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The damage spreading method (DS) provided a useful tool to obtain analyticalresults of the thermodynamics and stability of the 2D Ising model --amongstmany others--, but it suffered both from ambiguities in its results and fromlarge computational costs. In this paper we propose an alternative method, theso called self-overlap method, based on the study of correlation functionsmeasured at subsequent time steps as the system evolves towards itsequilibrium. Applying markovian and mean field approximations to a 2D Isingsystem we obtain both analytical and numerical results on the thermodynamicsthat agree with the expected behavior. We also provide some analytical resultson the stability of the system. Since only a single replica of the system needsto be studied, this method would seem to be free from the ambiguities thatafflicted DS. It also seems to be numerically more efficient and analyticallysimpler.

Self-overlap as a method of analysis in Ising models