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We describe a rigorous argument establishing the Berezinski-Kosterlitz-Thouless transition in a class of two-dimensional models including the plane rotator and the Coulomb gas. The main idea is to rewrite correlations in the Coulomb gas as super-positions of correlations in gases of neutral molecules of variable size and small effective activity.
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Fröhlich et al. (1981) studied this question.
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