Convergence of grand canonical Gibbs measures
The paper tries to prove existence of Gibbs states in continuum systems by adding a hard-core N-body potential with fixed radius and then letting N tend to infinity. In the presence of such a hard-core the existence is established, but unfortunately there is an error in the proof ot the crucial approximation lemma 3.1. More precisely, the inequality (3.10) does not hold uniformly in k except in the one-dimensional case. A note of this mistake is given also by the author in the paper ''Uniqueness of one dimensional continuum Gibbs states'', to appear in Commun. Math. Phys. However, since there is no counterexample, it remains open if such an approximation by hard-core potentials is possible or not.
scientific article; zbMATH DE number 3856169
scientific article