2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79188We discuss the interrelation between phase transitions in interacting lattice or continuum models, and the existence of infinite clusters in suitable random-graph models. In particular, we describe a random-geometric approach to the phase transition in the continuum Ising model of two species of particles with soft or hard interspecies repulsion. We comment also on the related area-interaction process and on perfect simulation.Survey article, 25 pagesProbability60G55, 60K35; 82B05text