  Populations of heterogeneous, noisy oscillators on a two-dimensional lattice
display short-range order. Here, we show that if the oscillators are allowed to
actively move in space, the system undergoes instead a
Berezenskii-Kosterlitz-Thouless transition and exhibits quasi-long-range order.
This fundamental result connects two paradigmatic models -- XY and Kuramoto
model -- and provides insight on the emergence of order in active systems.
