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Conformal boundary conditions in the critical O(n) model and dilute loop models

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Figure 1: Phase diagram of the O (n) model with bulk spin coupling x and boundary spin coupling y
Figure 2: The ordinary (a) and extraordinary (b) boundary conditions for the dilute loop model.
Figure 3: Influence of the surface monomer fugacity y in the dilute (a) and dense phase (b) of the O (n) loop model
Figure 4: Generic phase diagram for 0 < n 1 < n in the rotated (y n 1 , y n − n 1 ) plane.
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