The Berezinskii-Kosterlitz-Thouless transition and correlations in the $XY$ kagomé antiferromagnet

The problem of the Berezinskii–Kosterlitz–Thouless transition in the highly frustrated $XY$ kagomé antiferromagnet is solved. The transition temperature is found. It is shown that the spin correlation function exponentially decays with distance even in the low-temperature phase, in contrast to the order parameter correlation function, which decays algebraically with distance.