Abstract
A set of renormalization equations for the two-dimensional Coulomb gas is derived which explicitly includes a large-distance cut-off in the bare interaction. The equations are solved numerically and the possibility of a new universal discontinuity at the Kosterlitz-Thouless transition emerges. The large-distance cut-off is related to finite size effects for the vortex renormalization of superconducting films and 4He films. The finite size effects are found to survive to macroscopic length scales and consist of two competing effects. The relative size of these two effects is inferred from the solution of the equations.
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