Renormalization transformation for the discrete gaussian model

A position-space renormalization transformation is obtained for the discrete gaussian model by a bond moving approximation. Our results can be translated in terms of the Coulomb gas, which is related to the discrete gaussian model, and yield in the low density regime of that model a behaviour which is qualitatively the same as that previously obtained by Kosterlitz on the basis of a density expansion. The present renormalization transformation can also be analyzed in a region of the discrete gaussian model that corresponds to a high density region of the Coulomb gas.