The critical correlation exponent of the planar XY model

For the ordinary nearest-neighbor XY model on the square lattice, we prove the Berezinskii–Kosterlitz–Thouless prediction that the critical spin-correlation exponent is 1/4. More precisely, at the mass-defined critical inverse temperature, the infinite-volume correlation is $n^{-1/4+o(1)}$. The infinite-volume limit through free square boxes is taken before the separation limit.