2D classical XY model $$H = -J\cos(\theta_{i}-\theta_{j})%$$ is famous for Berezinskii-Kosterlitz-Thouless phase transition. This is because of the difference of correlation function between hot and low limit. At low limit correlation function is written as $$G(\boldsymbol{r}) \sim \left(\frac{1}{r}\right)^{\frac{1}{2\pi\beta J}}$$ I can't derive it. Please teach me.
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