2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/228823Out of equilibrium magnetised solutions of the $XY$-Hamiltonian Mean Field ($XY$-HMF) model are build using an ensemble of integrable uncoupled pendula. Using these solutions we display an out-of equilibrium phase transition using a specific reduced set of the magnetised solutions.Statistical MechanicsChaotic DynamicsOut of Equilibrium Solutions in the $XY$-Hamiltonian Mean Field modeltext