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Monte Carlo study of the deconfined critical action phase diagram reveals a region where spinon deconfinement occurs through a weak first-order phase transition, in agreement with Ginzburg- Landau theory. Wilson renormalization argument in combination with the absence of the data collapse even in the regime of weak interaction between the spinons casts a serious doubt on the possibility of the continuous deconfinement transition. We also argue that if a continuous deconfined criticality does exist on the phase diagram, its nature is analogous, in a certain precise sense, to that of the XY universality class


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