  We consider the dipole-dipole correlations for the two-dimensional Coulomb
gas/sine-Gordon model for $\beta> 8\pi$ by a renormalization group method.
First we re-establish the renormalization group analysis for the partition
function using finite range decomposition of the covariance. Then we extend the
analysis to the correlation functions. Finally, we show a power-law decay
characteristic of the dipole gas.
