We consider spatial coarse-graining in statistical ensembles of non-selfintersecting and one-fold selfintersecting center-vortex loops as they emerge in the confining phase of SU(2) Yang-Mills thermodynamics. This coarse-graining is due to a noisy environment and described by a curve shrinking flow of center-vortex loops locally embedded in a two-dimensional flat plane. The renormalization-group flow of an effective `action, which is defined in purely geometric terms, is driven by the curve shrinking evolution. In the case of non-selfintersecting center-vortex loops, we observe critical behavior of the effective `action as soon as the center-vortex loops vanish from the spectrum of the confining phase due to curve shrinking. This suggest the existence of an asymptotic mass gap. An entirely unexpected behavior in the ensemble of one-fold selfintersecting center-vortex loops is connected with the spontaneous emergence of order. We speculate that the physics of planar, one-fold selfintersecting center-vortex loops to be relevant for two-dimensional systems exhibiting high-temperature superconductivity.
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