Some AB-percolation problems in the antiferromagnetic potts model

The AB-correlated-site/random-bond percolation problem in a q-state antiferromagnetic Potts model on Bethe lattices is solved. We find the analytic expression of the AB-percolation characteristic functions in terms of the temperature, the external field and the active bond concentration p_B. The AB-threshold and the phase boundary of the system coincide at zero temperature and at most in two other points for every constant p_B > 1?σ. The properties of the Bethe lattice allow us to find the temperature dependent p_B which defines the AB-droplets, i.e. those special AB-clusters which diverge with thermal exponents along the phase boundary.