BKT transition for ${\mathsf{S}\mathsf{i}\mathsf{n}\mathsf{e}}_{\beta }$

We prove the Berezinskii-Kosterlitz-Thouless (BKT) phase transition in the large-distance behaviour of the two-point correlation function of the ${\mathsf{S}\mathsf{i}\mathsf{n}\mathsf{e}}_{\beta }$ point process for all $\beta >0$, confirming the first term of an asymptotic expansion predicted by Forrester.