2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/184882We extend a Gaussian model for the internal electrical potential of a two-dimensional Coulomb gas by a non-Gaussian measure term, which singles out the physically relevant configurations of the potential. The resulting Hamiltonian, expressed as a functional of the internal potential, has a surprising large-scale limit: The additional term simply counts the number of maxima and minima of the potential. The model allows for a transparent derivation of the divergence of the correlation length upon lowering the temperature down to the Kosterlitz-Thouless transition point.final version, extended discussion, appendix added, 8 pages, no figure, uses IOP documentclass iopartStatistical Mechanicstext