2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71868We consider two-dimensional marked point processes which are Gibbsian with a two-body-potential U. U is supposed to have an internal continuous symmetry. We show that under suitable continuity conditions the considered processes are invariant under the given symmetry. We will achieve this by using Ruelle`s superstability estimates and percolation arguments.22 pagesProbabilityMathematical Physics60K35; 82B21; 82B26text