Antipercolation on Bethe and triangular lattices

The antipercolation problem is solved on the Bethe lattice. The critical exponents are identical to the percolation exponents when the coordination number z is greater than a critical value z c =3, for which the problem has new exponents satisfying extended universality and below which there is no transition. For alternate lattices the problem may be transformed into a percolation problem with different occupation probabilities on the two sublattices. This allows a connection with an s-state Potts model with different z-spin interactions on the two sublattices. In two dimensions there is no transition on the alternate square and honeycomb lattices whereas a transition exists on the triangular lattice. Using the phenomenological renormalisation group method, the critical concentration is found to be p c (a) =0.21 whereas the correlation length exponent nu a seems to converge towards the accepted percolation value nu p =1.333.