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We introduce a lattice spin model that mimics a system of interactingparticle through a short range repulsive potential and a long range attractivepower law decaying potential. We performed a detailed analysis of the generalequilibrium phase diagram of the model at finite temperature, showing that theonly possible equilibrium pases are the ferromagnetic and the antiferromagneticones. We then studied the non equilibrium behavior of the model after a quenchto subcritical temperatures, in the antiferromagnetic region of the phasediagram region, where the pair interaction potential behaves in the samequalitative way as in a Lennard-Jones gas. We found that, even in the absenceof quenched disorder or geometric frustration, the competition betweeninteractions gives rise to non--equilibrium disordered structures at low enoughtemperatures that strongly slow down the relaxation of the system.

Non-equilibrium structures and slow dynamics in a two dimensional spin system with competitive long range and short range interactions