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The statistical mechanics of polymer loops entangled in the two-dimensional array of randomly distributed obstacles of infinite length is discussed. The area of the loop projected onto the plane perpendicular to the obstacles is used as a collective variable in order to re-express a (mean-field) effective theory for the polymer conformation. It is shown explicitly that the loop undergoes a collapse transition to a randomly branched polymer with .
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Otto et al. (1996) studied this question.
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