Abstract: In this joint work with Isabel Rios we prove the existence and uniqueness of equilibrium states associated to Holder continuous potentials with small variation for a family of partially hyperbolic systems. This family related to the three-dimensional horseshoe introduced by Díaz, Horita, Sambarino and Rios in 2009. The ergodic properties of this model were studied by Leplaideur, Oliveira and Rios in 2011. In this last work, the authors proved the existence of a regular potential (with big variation) which has two mutually singular equilibrium states.