This article presents a study of the equivalence between the sine-Gordon model and Coulomb systems. For this, we started from the grand canonical partition function of the particle theory in which the Coulomb systems are found and, through the Hubbard-Stratonovich transformation, we arrived at a canonical partition function in the field theory, where it was shown that the sine-Gordon model is equivalent to the field model of Coulomb systems, because both partition functions coincide. From this it is possible to find applications of the sine-Gordon model, a widely studied model, to the study of Coulomb systems.