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The existence of a discontinuity in the inverse dielectric constant of thetwo-dimensional Coulomb gas is demonstrated on purely numerical grounds. Thisis done by expanding the free energy in an applied twist and performing afinite-size scaling analysis of the coefficients of higher-order terms. Thephase transition, driven by unbinding of dipoles, corresponds to theKosterlitz-Thouless transition in the 2D XY model. The method developed is alsoused for investigating the possibility of a Kosterlitz-Thouless phasetransition in a three-dimensional system of point charges interacting with alogarithmic pair-potential, a system related to effective theories oflow-dimensional strongly correlated systems. We also contrast the finite-sizescaling of the fluctuations of the dipole moments of the two-dimensionalCoulomb gas and the three-dimensional logarithmic system to those of thethree-dimensional Coulomb gas.Comment: 15 pages, 16 figure

Instanton correlators and phase transitions in two- and three-dimensional logarithmic plasmas