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