  We study a repulsive thermal system governed by odd interactions. The
interplay between oddness and inertia induces a non-equilibrium phase
transition from a homogeneous to a non-homogeneous phase, characterized by
bubbles induced by odd interactions. This phenomenon occurs in the absence of
attractions and is generated by the competition between the standard pressure
contribution due to particle repulsion and an effective surface tension
generated by odd-induced centrifugal forces. As a signature of the phase
transition, the system exhibits vortex structures and oscillating spatial
velocity correlations, which emerge close to the analytically predicted
transition point. Our findings can be verified in granular experiments governed
by odd interactions, such as spinners and colloidal magnets, and could be key
to characterizing the emerging properties of metamaterials.
