In this talk we will define a model of n interacting particles at positive temperature. We will study its macroscopic behavior as n grows to infinity by injecting, modulo permutations, the n-particle space into the space of probability measures. This sequence of models satisfy a Laplace principle and, in consequence, a large deviation principle which implies, in some cases, an almost sure convergence of the random n-particle state to a deterministic probability measure. This talk will be based on arXiv:1703.02680