Abstract
A new set of renormalization equations for the two-dimensional Coulomb gas is derived. Within this new description, the prediction of a universal jump or the prediction that the exponent $\ensuremath{\eta}$ is \textonequarter{} at the critical line breaks down below a certain temperature. Consequently it should be possible to have a Kosterlitz-Thouless transition without a universal jump. A realization is suggested.
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