Partial Breaking of Three-Fold Symmetry via Percolation of a Domain Wall

We show that suppression of vortex strings splits the order-disorder transition in the three-state Potts ferromagnet on a simple cubic lattice and opens up an intermediate phase characterized by partial breaking of the three-fold symmetry and long-range order. In contrast, suppression of vortices in the same model on a square lattice results in an intermediate phase with enhanced U(1) symmetry and quasi-long-range order. We show that the difference between the two phases originates from distinct patterns of domain wall proliferation. A domain wall, separating the two most populous spin states, percolates on its own in the former phase but remains at a percolation threshold in the latter.