Restoration of Gibbsianness for projected and FKG renormalized measures
The variational approach for almost quasilocal measures is studied. The authors establish conditions for the validity of the usual (specification-dependent) variational principle when a zero relative entropy density implies consistency with the same specification. The main theorem relates this implication to concentration properties of finite-volume relative densities. In order to apply this result the authors consider specifications that are monotonicity preserving in FKG sense and show that implications of the theorem regarding the almost quasilocality of the consistent measures. In the next application the monotonicity condition is replaced by the existence of appropriate ``continuity rates''. In particular, it is obtained that for projections to a line ``zero entropy density implies consistency with the same specification'' without any support assumption.
scientific article; zbMATH DE number 2101599