We present a lattice spin model that mimics a system of interacting particles through a short-range repulsive potential and a long-range attractive power-law decaying potential. We perform a detailed analysis of the general equilibrium phase diagram of the model at finite temperature, showing that the only possible equilibrium phases are the ferromagnetic and the antiferromagnetic ones. We then study the nonequilibrium behavior of the model after a quench to subcritical temperatures, in the antiferromagnetic region of the phase diagram region, where the pair interaction potential behaves in the same qualitative way as in a Lennard-Jones gas. We find that even in the absence of quenched disorder or geometric frustration, the competition between interactions gives rise to nonequilibrium disordered structures at low enough temperatures that strongly slow down the relaxation of the system. This nonequilibrium state presents several features characteristic of glassy systems such as subaging, nontrivial fuctuation dissipation relations, and possible logarithmic growth of free-energy barriers to coarsening.

• Received 21 November 2008

DOI:https://doi.org/10.1103/PhysRevE.80.021114