Clustering and phase transitions in a 2D superfluid with immiscible active impurities

Phase transitions of a finite-size two-dimensional superfluid of bosons in presence of active impurities are studied by using the projected Gross–Pitaevskii model. Impurities are described with classical degrees of freedom. A spontaneous clustering of impurities during the thermalization is observed. Depending on the interaction among impurities, such clusters can break due to thermal fluctuations at temperatures where the condensed fraction is still significant. The emergence of clusters is found to increase the condensation transition temperature. The condensation and the Berezinskii–Kosterlitz–Thouless transition temperatures, determined numerically, are found to strongly depend on the volume occupied by the impurities: a relative increase up to a of their respective values is observed, whereas their ratio remains approximately constant. (paper)