Novel Dynamics and Thermodynamics in systems with long range interactions

Systems with long range interactions display some anomalies when its dynamics and thermodynamics are studied below certain conditions. Among these anomalies are the quasi- stationary states, which are exacerbated because of special initial conditions that are used here. We present in this letter a new Hamiltonian whose potential is inspired in the two-dipole interaction. An analytical solution is obtained for the equilibrium in the canonical ensemble that is coincident with the one obtained from computational simulations. However, results from this model presents a kind of nonequivalence of ensembles in long-living states before arriving to equilibrium. Thus, a complete characterization is made for the nonequilibrium through molecular dynamics. In which, novel quasi-stationary states are observed due to the long range interactions.