  The motion of active colloids is generally achieved through their anisotropy,
as exemplified by Janus colloids. Recently, there was a growing interest in the
propulsion of isotropic colloids, which requires some local symmetry breaking.
Although several mechanisms for such propulsion were proposed, little is known
about the role played by the interactions within the environment of the
colloid, which can have a dramatic effect on its propulsion. Here, we propose a
minimal model of an isotropic colloid in a bath of solute particles that
interact with each other. These interactions lead to a spontaneous phase
transition close to the colloid, to directed motion of the colloid over very
long timescales and to significantly enhanced diffusion, in spite of the
crowding induced by solute particles. We determine the range of parameters
where this effect is observable in the model, and we propose an effective
Langevin equation that accounts for it and allows one to determine the
different contributions at stake in self-propulsion and enhanced diffusion.
