Asymptotic behavior of Gibbsian distributions for lattice systems and its dependence on the form of the volume

A study is made of the cases for which the existence of Gibbsian states in an infinite lattice was proved in earlier papers. It is proved that Gibbstan states exist in an infinite region, which may be part of the complete lattice, and an investigation is made of the dependence of the correlation functions on the form of the region. The second term in the asymptotic behavior of the free energy, which depends on the form of the region, is found. Finally, some properties of correlation weakening for such Gibbsian states are investigated.