# Non-local order parameter for Kosterlitz–Thouless transition

It is known, that there's no local order parameter in Kosterlitz-Thouless transition.

Is the order parameter in Kosterlitz-Thouless transition non-local?

Correlation function have different behaviour: $$\langle\psi(x)\psi^\dagger(y)\rangle \sim \frac{e^{-r/\xi}}{\sqrt{r}} \;\;\;\;\;\;\;\;\;\; T \gg T_c$$ $$\langle\psi(x)\psi^\dagger(y)\rangle \sim \frac{1}{r^\eta} \;\;\;\;\;\;\;\;\;\; T\ll T_c$$