2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/132383The conservation of translation as a symmetry in two-dimensional systems with interaction is a classical subject of statistical mechanics. Here we establish such a result for Gibbsian particle systems with two-body interaction, where the interesting cases of singular, hard-core and discontinuous interaction are included. We start with the special case of pure hard core repulsion in order to show how to treat hard cores in general.44 pages, 6 figuresProbabilityMathematical Physics82B21 (Primary), 82B26, 82B31, 60K35 (Secondary)text