  Using elementary methods we obtain a power-law lower bound on the two-point
function of the planar XY spin model at low temperatures. This was famously
first rigorously obtained by Fr\"{o}hlich and Spencer and establishes a
Berezinskii-Kosterlitz-Thouless phase transition in the model. Our argument
relies on a new loop representation of spin correlations, a recent result of
Lammers on delocalisation of integer-valued height functions, and classical
correlation inequalities.
