Relative Energies for Non-Gibbsian States

We investigate the suggestion of R.L. Dobrushin, that for many examples of non-Gibbsian measures, a well-defined interaction potential can still be derived. Such an interaction cannot be absolutely summable, uniformly in all configurations. Rather there will exist a typical set of configurations on which the interaction decays sufficiently fast. We show how to construct an interaction, using quite elementary methods, for example of the restriction of the Ising pure phases to one layer of the lattice. We sketch a general setup, showing that there is an intimate relation between the problem treated here and the decay of correlations in certain disordered systems. Received: 27 March 1996 / Accepted: 29 July 1996