Percolation and Gibbs states multiplicity for ferromagnetic Ashkin – Teller models

For a region of the nearest-neighbour ferromagnetic Ashkin–Teller spin systems on Z2, we characterize the existence of multiple Gibbs states via percolation. In particular, there are multiple Gibbs states if and only if there exists percolation of any of the spin types (i.e. the magnetized states are characterized by percolation of the dominant species). This result was previously known only for the Potts models on Z2.