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We study the properties of a simple lattice model of repulsive particlesdiffusing in a pinning landscape. The behaviour of the model is very similar tothe observed physics of vortices in superconductors. We compare and discuss theequilibrium phase diagram, creep dynamics, the Bean state profiles, hysteresisof magnetisation loops (including the second peak feature), and, in particular,``off equilibrium'' relaxations. The model is analytically tractable in replicamean field theory and numerically via Monte Carlo simulations. It offers acomprehensive schematic framework of the observed phenomenology

Off-equilibrium magnetic properties in a model of repulsive particles for vortices in superconductors