Maes C. , Vande Velde K.
Relative energies for non-Gibbsian states
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ABSTRACT. We investigate the suggestion of R.L. Dobrushin, that for many
examples ofnon-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
configurationson which the interaction decays sufficiently.
We are showing how to complete this program, using quite elementary
methods,for the example of the restriction of the Ising pure
phases to one layer of the lattice. We also treat the Ising
pure phases under Kadanoff transformation with block-size one and a toy
model.
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.